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A note on the solvability of double saddle-point problems Appl. Math. Lett. (IF 3.7) Pub Date : 2024-04-16 Siqi Liang, Na Huang
We derive the necessary conditions and a sufficient condition for the nonsingularity of a class of block three-by-three saddle-point problems. When it is singular, the sufficient conditions for the solvability are also discussed.
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Nontrivial solutions for indefinite Schrödinger–Poisson systems and Kirchhoff equations Appl. Math. Lett. (IF 3.7) Pub Date : 2024-04-15 Shuai Jiang
In this paper we consider 4-superlinear Schrödinger–Poisson systems. The potential here is indefinite so that the Schrödinger operator possesses a finite-dimensional negative space. By Morse theory, we obtain the existence of nontrivial solutions for this problem. Similar result for Kirchhoff equations on is also presented.
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A phase velocity preserving fourth-order finite difference scheme for the Helmholtz equation with variable wavenumber Appl. Math. Lett. (IF 3.7) Pub Date : 2024-04-12 Tingting Wu, Wenhui Zhang, Taishan Zeng
Numerically solving the Helmholtz equation with large wavenumbers can be challenging due to the highly oscillatory nature of the solution. This paper proposes a 3-point finite difference scheme for numerically solving the 1D Helmholtz equation with variable wavenumber. The proposed scheme preserves the phase velocity, making it well-suited for problems with large wavenumbers. Convergence analysis shows
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Analysis of a nonlocal diffusion model with a weakly singular kernel Appl. Math. Lett. (IF 3.7) Pub Date : 2024-04-09 Jinhong Jia, Zhiwei Yang, Hong Wang
We establish that , the solution of a nonlocal diffusion model with a weakly singular kernel converges asymptotically to the solution of the corresponding Fickian diffusion equation. The diffusion tensor of the Fickian equation is determined by half of the covariance matrix, with serving as the probability density function. Numerical experiments are performed to validate our findings. Additionally
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Finite termination of the optimal solution sequence in parametric optimization Appl. Math. Lett. (IF 3.7) Pub Date : 2024-04-06 Ruyu Wang, Wenling Zhao, Yaozhong Hu
This paper investigates the finite termination of the optimal solution sequence in parametric optimization as a subproblem of the equilibrium problems. By introducing an augmented mapping on the solution set of the equilibrium problems, we establish the concept of augmented weak sharpness for this set relative to the sequence of optimal solutions in parametric optimization. Augmented weak sharpness
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On the uniqueness of 3-D inhomogeneous viscous incompressible magnetohydrodynamic equations with bounded density Appl. Math. Lett. (IF 3.7) Pub Date : 2024-04-05 Xiaojie Wang, Fuyi Xu
In this paper, we prove the uniqueness of the global solutions constructed by Xu et al. (2022).
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A modified partially randomized extended Kaczmarz iteration method Appl. Math. Lett. (IF 3.7) Pub Date : 2024-04-04 Fang Chen, Jin-Feng Mao
The partially randomized extended Kaczmarz method is effective for solving large, sparse, overdetermined and inconsistent linear systems. In this paper, we propose a modified variant for this method, and give a tight upper bound for its convergence rate. Moreover, we verify the efficiency of the proposed method by numerical experiments.
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New exponentially weighted inequality and its application to finite-time stability of descriptor time-delay systems Appl. Math. Lett. (IF 3.7) Pub Date : 2024-04-04 Yusheng Jia, Chong Lin
The paper considers the finite-time stability of descriptor time-delay systems. Firstly, we establish a set of exponentially weighted orthogonal polynomials, and based on this, we obtain a new exponentially weighted inequality(EWI). Secondly, an augmented Lyapunov-like functional (LLF) is established driven by the presented EWI. Finally, by applying the EWI and the LLF, some sufficient conditions for
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Blow-up of solutions to the Keller–Segel model with tensorial flux in high dimensions Appl. Math. Lett. (IF 3.7) Pub Date : 2024-04-02 Valeria Cuentas, Elio Espejo, Takashi Suzuki
Over the course of the last decade, there has been a significant level of interest in the analysis of Keller–Segel models incorporating tensorial flux. Despite this interest, the question of whether finite-time blowup solutions exist remains a topic of ongoing research. Our study provides evidence that solutions of this nature are indeed possible in dimensions when utilizing a tensorial flux expressed
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Self-similar solutions and large time behavior to the 2D isentropic compressible Navier–Stokes equations with vacuum free boundary and rotation Appl. Math. Lett. (IF 3.7) Pub Date : 2024-03-30 Kunquan Li, Dongfu Tong, Zhengguang Guo
This paper is concerned with a class of self-similar analytical solutions to the 2D isentropic compressible Navier–Stokes equations with vacuum free boundary for polytropic gases. It is shown that the free boundary will grow linearly in time (see (1.11)), moreover, both angular velocity and its derivatives, and the derivative of radial velocity will tend to zero as , while radial velocity itself is
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Construction of a modified butterfly subdivision scheme with [formula omitted]-smoothness and fourth-order accuracy Appl. Math. Lett. (IF 3.7) Pub Date : 2024-03-30 Byeongseon Jeong, Hyoseon Yang, Jungho yoon
This article presents a modified butterfly subdivision scheme with improved smoothness over regular triangular meshes. The proposed technique is an approximating scheme with a tension parameter. It achieves fourth-order accuracy and generates limit surfaces for a suitable range of the parameter while maintaining the same support of the original butterfly scheme. To validate the theoretical results
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Power-series solution of the L-fractional logistic equation Appl. Math. Lett. (IF 3.7) Pub Date : 2024-03-30 Marc Jornet, Juan J. Nieto
We consider the L-fractional derivative, which has been proposed in the literature to study fractional differentials in geometry and processes in mechanics. Our context is population growth and epidemiology, for which the use of L-derivatives is motivated by transitions. Using power series, we solve the logistic differential equation model under this fractional derivative. Several conclusions on the
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Analysis of a higher order problem within the second gradient theory Appl. Math. Lett. (IF 3.7) Pub Date : 2024-03-30 J.R. Fernández, R. Quintanilla
In this note, we study analytically a higher order equation in a semi-infinite cylinder. First, we will recall some basic inequalities and we define the adequate energy function that we need to find our estimates. Then, the spatial energy decay is proved to be of exponential type. Finally, we consider the application to some heat conduction problems.
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Dynamics of a Fokker–Planck type diffusion epidemic model with general incidence and relapse Appl. Math. Lett. (IF 3.7) Pub Date : 2024-03-27 Qian Ding, Jianshe Yu, Kai Wang
In this paper, a spatially heterogeneous SIRI epidemic model with general morbidity is studied, which conforms to the Fokker–Planck type diffusion law. The basic reproduction number of the model is introduced, and the threshold dynamics based on is discussed. In particular, with the help of elliptic eigenvalue theory, we determine the asymptotic profiles of the endemic equilibrium when the diffusion
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Normalized solutions and least action solutions for Kirchhoff equation with saturable nonlinearity Appl. Math. Lett. (IF 3.7) Pub Date : 2024-03-27 Jiexiong Jin, Guofeng Che
In this paper, we are concerned with the existence of solutions for the following Kirchhoff type equation with saturable nonlinearity: where , and is a parameter. By imposing some suitable conditions on the function , we obtain the existence of normalized solutions and least action solutions for the above problem. Some related results are greatly improved and extended.
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Nonstationary asymptotical regularization method with convex constraints for linear ill-posed problems Appl. Math. Lett. (IF 3.7) Pub Date : 2024-03-27 Muyi Liu, Shanshan Tong, Wei Wang
We investigate the method of nonstationary asymptotical regularization for solving linear ill-posed problems in Hilbert spaces. This method introduces the convex constraints that are proper lower semicontinuous and allowed to be non-smooth, therefore can be used for sparsity and discontinuity reconstruction. Under some suitable conditions , the convergence and regularity of the proposed method are
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Symmetry study of a novel integrable supersymmetric dispersionless system Appl. Math. Lett. (IF 3.7) Pub Date : 2024-03-26 Zitong Chen, Man Jia, Ruoxia Yao, S.Y. Lou
A novel integrable supersymmetric dispersionless fermion system is proposed and studied by means of symmetry approach and the bosonization method, which is integrable under the meaning of possessing infinitely many higher order symmetries. It is shown that there are some types of infinitely many symmetries with arbitrary functions. The first type of infinitely many symmetries commutes each other, whereas
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Threshold behaviors and density function of a stochastic parasite-host epidemic model with Ornstein–Uhlenbeck process Appl. Math. Lett. (IF 3.7) Pub Date : 2024-03-26 Xiaoshan Zhang, Xinhong Zhang
In this paper, a stochastic parasite-host epidemic model is investigated. To simulate the unavoidable effects of environmental perturbations on the model, the disease transmission rate is assumed to satisfy a log-normal Ornstein–Uhlenbeck process. We study the stationary distribution and extinction of the disease and find a critical value , which serves as a threshold determining the persistence or
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Error estimates of compact and hybrid Richardson schemes for the parabolic equation Appl. Math. Lett. (IF 3.7) Pub Date : 2024-03-26 Qifeng Zhang
Hybrid time integration has received more and more attention in recent years due to its inherent computational advantages including all-at-once implementation and without need of multiple start values. In this letter we establish the compact and hybrid Richardson schemes and show that they are unconditionally convergent in theory under the framework of the energy method for the first time to solve
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Propagation dynamics of a free boundary problem in advective environments Appl. Math. Lett. (IF 3.7) Pub Date : 2024-03-25 Xueqi Fan, Ningkui Sun, Di Zhang
In this paper, we study the equation in the domain , where is the free boundary and . The influence of the advection coefficient on the propagation dynamics of the solutions is considered. We find two parameters 2 and such that when , only spreading happens; when , there is a virtual spreading-transition-vanishing trichotomy result; when , only vanishing happens.
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Stability of traveling wavefronts for advection–reaction–diffusion equation Appl. Math. Lett. (IF 3.7) Pub Date : 2024-03-22 Ming Mei, Ruijun Xie
In this paper, we study an advection–reaction–diffusion equation, where the nonlinear advection has neither monotonicity nor variational structure. For all wavefronts with the speed , where is the minimal wave speed, we use the technical weighted energy method to prove that these wavefronts are exponentially stable, when the initial perturbations are small in a weighted Sobolev space.
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A nonlinear elliptic equation with a degenerate diffusion and a source term in [formula omitted] Appl. Math. Lett. (IF 3.7) Pub Date : 2024-03-22 Guillaume Leloup, Roger Lewandowski
We study a simplified equation governing turbulent kinetic energy in a bounded domain, arising from turbulence modeling where the eddy diffusion is given by , with representing the Prandtl mixing length of the order of the distance to the boundary, and a right-hand side in . We obtain estimates of in spaces and we establish the convergence toward the formal limit equation in the sense of the distributions
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An immersed boundary-phase field fluid-surfactant model with moving contact lines on curved substrates Appl. Math. Lett. (IF 3.7) Pub Date : 2024-03-22 Yanyao Wu, Zhijun Tan
In this study, we propose an immersed boundary-phase field fluid-surfactant model that incorporates moving contact lines on complex geometries. To accurately capture the interface, we introduce an additional phase field variable to represent the solid phase, which remains fixed throughout the process. The modified Cahn–Hilliard equations are utilized to describe the interface. In order to address stiffness
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A high-order limiter-free arbitrary Lagrangian–Eulerian discontinuous Galerkin scheme for compressible multi-material flows Appl. Math. Lett. (IF 3.7) Pub Date : 2024-03-22 Xiaolong Zhao, Dongyang Shi, Shicang Song, Shijun Zou
In this paper, a high-order limiter-free arbitrary Lagrangian–Eulerian discontinuous Galerkin (ALE-DG) scheme is proposed for simulating one-dimensional compressible multi-material flows. The system is discretized by the DG method, and a kind of Taylor’s expansion basis functions in the general cell is used to construct the interpolation polynomials of the variables. The mesh velocity at the node recognized
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Boundedness in a chemotaxis-May–Nowak model with exposed state Appl. Math. Lett. (IF 3.7) Pub Date : 2024-03-21 Qingshan Zhang, Yan Li
This paper is concerned with the Neumann initial–boundary value problem of the chemotaxis-May–Nowak model with exposed state for virus dynamics. It is proved that the problem admits a unique global classical solution which is uniformly bounded for all sufficiently smooth initial data in smoothly bounded domains , .
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Mittag-Leffler kernel-based oversampling collocation method for fractional initial value problems with contaminated data Appl. Math. Lett. (IF 3.7) Pub Date : 2024-03-21 X.Y. Li, B.Y. Wu, X.Y. Liu
Mittag-Leffler RKFs were introduced by Rosenfeld et al. based on the RKFs, a numerical approach called kernelized ABM was developed for solving fractional initial value problems (FIVPs). However, the accuracy of the obtained approximate solution degraded when the fractional order tends to small values. By employing the Mittag-Leffler RKFs, we develop an oversampling collocation technique for Caputo
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Sharp analysis of [formula omitted] method on graded mesh for time fractional parabolic differential equation Appl. Math. Lett. (IF 3.7) Pub Date : 2024-03-19 Jiliang Cao, Wansheng Wang, Aiguo Xiao
In this paper, we study the method for solving numerically a class of time fractional parabolic differential equations on a graded mesh. Based on the nonsmooth regularity assumptions, the stability and convergence of the proposed numerical method are investigated. Using rigorous and sharp theoretical analysis, we obtain the optimal graded parameter of the graded mesh. Numerical experiments are given
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A priori estimates and existence of solutions to a system of nonlinear elliptic equations Appl. Math. Lett. (IF 3.7) Pub Date : 2024-03-16 Yongsheng Jiang, Na Wei, Yonghong Wu
We consider the following nonlinear elliptic equations
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About stabilization by Poisson’s jumps for stochastic differential equations Appl. Math. Lett. (IF 3.7) Pub Date : 2024-03-16 Leonid Shaikhet
The well-known effect of stabilization by noise for Ito’s stochastic differential equations was proven by R.Z. Khasminskii more than 50 years ago. Here this effect is extended to stochastic differential equations with the Wiener process and Poisson’s measure. The obtained results are illustrated by examples with stabilization by Poisson’s jumps only or by white noise and Poisson’s jumps together. Some
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An equivalent formulation of Sonine condition Appl. Math. Lett. (IF 3.7) Pub Date : 2024-03-15 Xiangcheng Zheng
Sonine kernel is characterized by the Sonine condition (denoted by SC) and is an important class of kernels in nonlocal differential equations and integral equations. This work proposes a SC with a more general form (denoted by gSC), which is more convenient than SC to accommodate complex kernels and equations. A typical kernel is given, and the first-kind Volterra integral equation under gSC is accordingly
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An effective numerical method for the vector-valued nonlocal Allen–Cahn equation Appl. Math. Lett. (IF 3.7) Pub Date : 2024-03-15 Chen Cui, Yaoxiong Cai, Bo Tang
Nonlocal Allen–Cahn model and their numerical schemes have received great attention in the literature as nonlocal model becomes popular in various fields. Our main idea in this work is to consider the vector-valued nonlocal Allen–Cahn model, which is a coupled system of nonlinear partial differential equations. Then, with the help of the operator splitting method and finite difference method, a fully-decoupled
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Quasi-stationary distribution of a single species model under demographic stochasticity and Allee effects Appl. Math. Lett. (IF 3.7) Pub Date : 2024-03-15 Yu Zhu, Tao Feng
In this paper, we utilize an absorbed diffusion process to model the dynamics of a single species under the influence of demographic stochasticity and component Allee effects. The trajectories of stochastic solutions exhibits multi-scale dynamics distinct from those of the corresponding mean-field model. The primary focus is on analyzing transient dynamics before extinction, which is described by the
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On the composite waves of the two-dimensional pseudo-steady van der Waals gas satisfied Maxwell’s law Appl. Math. Lett. (IF 3.7) Pub Date : 2024-03-14 Shuangrong Li, Wancheng Sheng
This paper is concerned with a model of phase transition, the Euler equations with van der Waals gas satisfied Maxwell’s law. We study the composite waves for the two-dimensional (2D) Euler equations for pseudo-steady supersonic flow with van der Waals gas satisfied Maxwell’s law around a sharp corner. According to the initial value of the specific volume and the properties of van der Waals gas, the
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An enriched radial integration method for evaluating domain integrals in transient boundary element analysis Appl. Math. Lett. (IF 3.7) Pub Date : 2024-03-13 Bingrui Ju, Yan Gu, Ruzhuan Wang
Accurate evaluation of domain integrals is crucial for the overall accuracy of the boundary element method (BEM), particularly when dealing with dynamic problems and those involving body forces. The radial integration method (RIM) is a well-established and effective technique for computing domain integrals in boundary element analysis. When calculating domain integrals in transient problems, the integrand
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Normalized solutions to the Kirchhoff Equation with triple critical exponents in [formula omitted] Appl. Math. Lett. (IF 3.7) Pub Date : 2024-03-12 Xingling Fang, Zengqi Ou, Ying Lv
In this paper, we investigate the normalized solutions for the nonlinear critical Kirchhoff equations with combined nonlinearities: where , , and , , are constants. In , some interesting phenomena occur, which are, the -critical exponent for is , while the -critical exponent for is equal to the Sobolev critical exponent, i.e., . This paper investigates the case that the nonlinearity with triple critical
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Total and scattered field decomposition technique in mixed FETD methods and its applications for electromagnetic cloaks Appl. Math. Lett. (IF 3.7) Pub Date : 2024-03-12 Fuhao Liu, Wei Yang
In this paper, we apply the total and scattered field plane wave excitation method to the mixed finite element time-domain (FETD) method for solving Maxwell’s equations to compute the scattered field of electromagnetic cloaks. This method can quantify the performance and operating frequency range of the cloak. We also present a mixed FETD scheme, which is coupling with perfectly matched layers technique
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Positive solutions of parameter-dependent nonlocal differential equations with convolution coefficients Appl. Math. Lett. (IF 3.7) Pub Date : 2024-03-11 Xinan Hao, Xuhui Wang
In this paper we investigate a parameter-dependent nonlocal differential equations with convolution coefficients. Using the Birkhoff–Kellogg type theorem, existence of positive solutions is established. Under additional growth conditions, we obtain upper and lower bounds for the parameter. An example is also given to illustrate the main results.
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An energy estimate and a stabilized Lagrange–Galerkin scheme for a multiphase flow model Appl. Math. Lett. (IF 3.7) Pub Date : 2024-03-11 Aufa Rudiawan, Alexander Žák, Michal Beneš, Masato Kimura, Hirofumi Notsu
Multiphase flow models are commonly employed for understanding complex fluid flows, while few mathematical discussions exist. For a general multiphase flow model in Gidaspow (1994), an energy decay property is proved. A stabilized Lagrange–Galerkin scheme for the model and its stability property are presented. Here, a hyperbolic tangent transformation is employed to preserve the boundedness of the
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The (2+1)-dimensional generalized Benjamin–Ono equation: Nonlocal symmetry, CTE solvability and interaction solutions Appl. Math. Lett. (IF 3.7) Pub Date : 2024-03-11 Yueying Wu, Yunhu Wang
In this paper, the nonlocal symmetry of the (2+1)-dimensional generalized Benjamin–Ono equation are obtained by using the truncated Painlevé expansion. The nonlocal symmetry are localized by introducing auxiliary variables. Furthermore, this equation is also proved to be consistent expansion solvable, and three classes of exact solutions are derived.
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Oscillation of second-order trinomial differential equations with retarded and advanced arguments Appl. Math. Lett. (IF 3.7) Pub Date : 2024-03-07 Jozef Dzurina
In this paper we introduce new effective technique for investigation of oscillation for the second-order trinomial differential equation with retarded and advanced arguments Our criteria improve the existing ones and the progress is illustrated via several examples.
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A new kernel method for the uniform approximation in reproducing kernel Hilbert spaces Appl. Math. Lett. (IF 3.7) Pub Date : 2024-03-06 Woula Themistoclakis, Marc Van Barel
We are concerned with the uniform approximation of functions of a generic reproducing kernel Hilbert space (RKHS). In this general context, classical approximations are given by Fourier orthogonal projections (if we know the Fourier coefficients) and their discrete versions (if we know the function values on well-distributed nodes). In case such approximations are not satisfactory, we propose to improve
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Dispersive shock wave structure analysis for the defocusing Lakshmanan–Porsezian–Daniel equation Appl. Math. Lett. (IF 3.7) Pub Date : 2024-03-04 Yan Zhang, Hui-Qin Hao
Via the finite-gap integration theory, we study the defocusing Lakshmanan–Porsezian–Daniel (LPD) equation. Meanwhile, we derive the degenerate forms for the single-phase periodic solution. In addition, we obtain the basic and combined structures of the dispersive shock wave through the Whitham modulation equation parameterized by the Riemann invariant.
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Stability of impulsive stochastic functional differential equations with delays Appl. Math. Lett. (IF 3.7) Pub Date : 2024-03-04 Jingxian Guo, Shuihong Xiao, Jianli Li
In this paper, we consider the global asymptotical stability of stochastic functional differential equations with impulsive effects. First, by constructing the Lyapunov function, some stability criteria of impulsive stochastic functional differential equations are established. Second, we propose an application to investigate the effectiveness of the obtained results.
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A greedy average block sparse Kaczmarz method for sparse solutions of linear systems Appl. Math. Lett. (IF 3.7) Pub Date : 2024-03-04 A.-Qin Xiao, Jun-Feng Yin
A greedy average block sparse Kaczmarz method is developed for the sparse solution of the linear system of equations. The convergence theory of this method is established and the upper bound of its convergence rate with adaptive stepsize is derived. Numerical experiments are presented to verify the efficiency of the proposed method, which outperforms the existing sparse Kaczmarz methods in terms of
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Mass and energy conservative high-order diagonally implicit Runge–Kutta schemes for nonlinear Schrödinger equation Appl. Math. Lett. (IF 3.7) Pub Date : 2024-03-04 Ziyuan Liu, Hong Zhang, Xu Qian, Songhe Song
We present and analyze a series of structure-preserving diagonally implicit Runge–Kutta schemes for the nonlinear Schrödinger equation. These schemes possess not only high accuracy, high order convergence (up to fifth order) and efficiency due to the diagonally implicity but also mass and energy conservative properties. Theoretical analysis and numerical experiments are conducted to verify the accuracy
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Global existence for the stochastic rotation-two-component Camassa–Holm system with nonlinear noise Appl. Math. Lett. (IF 3.7) Pub Date : 2024-03-01 Yeyu Xiao, Yong Chen
We study the well-posedness for the stochastic rotation-two-component Camassa–Holm (R2CH) system with the nonlinear noise. We establish the local well-posedness of the stochastic R2CH system by the dispersion–dissipation approximation system and the regularization method. We also prove the global existence of the stochastic R2CH system with a large nonlinear noise.
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Stationary distribution analysis of a stochastic SIAM epidemic model with Ornstein–Uhlenbeck process and media coverage Appl. Math. Lett. (IF 3.7) Pub Date : 2024-02-28 Yilin Tian, Chao Liu, Lora Cheung
A stochastic SIAM (Susceptible individual-Infected individual-Aware individual-Media coverage) epidemic model with nonlinear disturbances is constructed, where awareness dissemination rate satisfies the mean-reverting Ornstein–Uhlenbeck process. Hybrid dynamic effects of Lévy jump and Ornstein–Uhlenbeck process on infectious disease transmission are discussed. By constructing appropriate stochastic
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Well-posedness for the stochastic Landau–Lifshitz–Bloch equation with helicity Appl. Math. Lett. (IF 3.7) Pub Date : 2024-02-27 Soham Sanjay Gokhale
We consider the stochastic Landau–Lifshitz–Bloch equation with helicity term driven by a real-valued Wiener process. We show the existence of a weak martingale solution, followed by pathwise uniqueness of the obtained solution, culminating into the existence of a strong solution using the theory of Yamada and Watanabe.
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The composite wave in the Riemann solutions for macroscopic production model Appl. Math. Lett. (IF 3.7) Pub Date : 2024-02-27 Zhijian Wei, Lihui Guo
In this paper, the Riemann solutions for the macroscopic production model with chaplygin gas under some special initial data are constructively obtained in the fully explicit form. An interesting composite wave is observed, it is formed by a rarefaction wave and a left-contact delta discontinuity attached to the wavefront of the rarefaction wave. Furthermore, this delta discontinuity gradually absorbs
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Sixth-order exponential Runge–Kutta methods for stiff systems Appl. Math. Lett. (IF 3.7) Pub Date : 2024-02-27 Vu Thai Luan, Trky Alhsmy
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The stabilized exponential-SAV approach for the Allen–Cahn equation with a general mobility Appl. Math. Lett. (IF 3.7) Pub Date : 2024-02-23 Yuelong Tang
In this paper, we construct a second-order accurate, energy stable and maximum bound principle-preserving scheme for the Allen–Cahn equation with a general mobility based on the stabilized exponential scalar auxiliary variable (SESAV) approach. Some extra stabilizing terms are added to the discretized scheme for the purpose of improving numerical stability. We first proved the maximum bound principle
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New Liouville-type theorem for the stationary tropical climate model Appl. Math. Lett. (IF 3.7) Pub Date : 2024-02-23 Youseung Cho, Hyunjin In, Minsuk Yang
We study the Liouville-type theorem for smooth solutions to the steady 3D tropical climate model. We prove the Liouville-type theorem if a smooth solution satisfies a certain growth condition in terms of -norm on annuli, which improves the previous results, Theorem 1.1 by Ding and Wu (2021), and Theorem 1.1 and Theorem 1.2 by Yuan and Wang (2023).
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Asymptotic analysis of time-fractional quantum diffusion Appl. Math. Lett. (IF 3.7) Pub Date : 2024-02-23 Peter D. Hislop, Éric Soccorsi
We study the large-time asymptotics of the mean-square displacement for the time-fractional Schrödinger equation in . We define the time-fractional derivative by the Caputo derivative. We consider the initial-value problem for the free evolution of wave packets in governed by the time-fractional Schrödinger equation , with initial condition , parameterized by two indices . We show distinctly different
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Global solvability for an indirect consumption chemotaxis system with signal-dependent motility Appl. Math. Lett. (IF 3.7) Pub Date : 2024-02-22 Ai Huang, Yifu Wang
This paper considers the indirect signal consumption-chemotaxis system with signal-dependent motility in a smooth bounded domain , as given by , where the motility function on , which generalizes . Based on point-wise positive lower bound estimate of , it is shown that for any suitably regular initial data, the corresponding initial–boundary value problem admits global smooth solutions.
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Dynamics for the diffusive logistic equation with a sedentary compartment and free boundary Appl. Math. Lett. (IF 3.7) Pub Date : 2024-02-22 Xueping Li, Lei Li, Mingxin Wang
This paper investigates the diffusive logistic equation with a sedentary compartment and free boundary whose dynamics has been considered by Wang and Cao (2015) when the intrinsic rate of reproduction in the stationary class is less than the rate of switching from stationary to mobile. However, the case is left as an open problem in Wang and Cao (2015). We shall show that spreading happens if and give
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Nonlocal symmetry and group invariant solutions of dissipative (2+1)-dimensional AKNS equation Appl. Math. Lett. (IF 3.7) Pub Date : 2024-02-21 Yarong Xia, Jiayang Geng, Ruoxia Yao
In this paper, the nonlocal symmetry of dissipative (2+1)-dimensional AKNS equation is constructed by auxiliary equation method. In order to better study new group invariant solutions of AKNS equation with the help of nonlocal symmetry, we introduce an new auxiliary dependent variable, the (2+1) dimensional AKNS equation is extended to a new closed prolonged system. Therefore, the nonlocal symmetry
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Periodic transmission theory of circularly symmetric multi-ring solitons in nonlinear Schrödinger equation Appl. Math. Lett. (IF 3.7) Pub Date : 2024-02-21 Jie Li, Zhi-Ping Dai, Zhen-Jun Yang
In this paper, the evolution characteristics of periodic transmission of circularly symmetric multi-ring solitons in optical nonlocal materials based on nonlinear Schrödinger equation are investigated in detail. The transmission expression of circularly symmetric multi-ring solitons has been derived. It was found that the number and size of rings in these solitons can be controlled by initial parameters
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Long-time asymptotics for the integrable nonlocal Lakshmanan–Porsezian–Daniel equation with decaying initial value data Appl. Math. Lett. (IF 3.7) Pub Date : 2024-02-20 Wei-Qi Peng, Yong Chen
In this work, we study the Cauchy problem of integrable nonlocal Lakshmanan-Porsezian-Daniel equation with rapid attenuation of initial data. The basic Riemann–Hilbert problem of integrable nonlocal Lakshmanan-Porsezian-Daniel equation is constructed from Lax pair. Using Deift-Zhou nonlinear steepest descent method, the explicit long-time asymptotic formula of integrable nonlocal Lakshmanan-Porsezian-Daniel
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Inverse scattering and soliton dynamics for the mixed Chen–Lee–Liu derivative nonlinear Schrödinger equation Appl. Math. Lett. (IF 3.7) Pub Date : 2024-02-20 Nan Liu, Jinyi Sun, Jia-Dong Yu
Under investigation in this letter is a mixed Chen–Lee–Liu derivative nonlinear Schrödinger equation which can be considered as the simplest model to approximate the dynamics of weakly nonlinear and dispersive waves, taking into account the self-steepening effect. The inverse scattering transform under the zero boundary conditions and analytical scattering coefficients with an arbitrary number of simple
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A randomized block extended Kaczmarz method with hybrid partitions for solving large inconsistent linear systems Appl. Math. Lett. (IF 3.7) Pub Date : 2024-02-20 Xiang-Long Jiang, Ke Zhang
We propose a randomized block extended Kaczmarz method with hybrid partitioning techniques for solving large inconsistent linear systems. It employs the -means clustering to partition the columns of the coefficient matrix while applying the uniform sampling to derive the row partition of the coefficient matrix. It is proved that the proposed algorithm converges to the unique least-squares least-norm