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Non-existence results for fourth order Hardy–Hénon equations in dimensions 2 and 3 J. Differ. Equ. (IF 2.4) Pub Date : 2024-03-19 Tran Thi Ngoan, Quôć Anh Ngô, Tran Van Tuan
We consider the fourth order Hardy–Hénon equation with , , and . This is the fourth order analogy of the second order equation , known as the Hardy–Hénon equation, which was proposed by Hénon in 1973 as a model to study rotating stellar systems in astrophysics. Although there have been many works devoting to the study of the above fourth order equation, the assumption is often assumed. In this work
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Hydrodynamic limit of the Maxwell-Schrödinger equations to the compressible Euler-Maxwell equations J. Differ. Equ. (IF 2.4) Pub Date : 2024-03-18 Jeongho Kim, Bora Moon
We present the hydrodynamic limit of the nonlinear Maxwell-Schrödinger equations. Under the boundedness assumption on the density, we show that the Maxwell-Schrödinger system converges to the compressible Euler-Maxwell system as the Planck constant tends to 0. Our analysis is based on the modulated energy estimate.
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Existence of radially symmetric blow-up solutions for quantum Zakharov system J. Differ. Equ. (IF 2.4) Pub Date : 2024-03-14 Koichi Komada
In this paper, we consider the quantum Zakharov system where and is a wave speed. We show blow-up or grow-up for the quantum Zakharov system with and with under the radial assumption when .
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Homogenisation of the Stokes equations for evolving microstructure J. Differ. Equ. (IF 2.4) Pub Date : 2024-03-14 David Wiedemann, Malte A. Peter
We consider the homogenisation of the quasi-stationary Stokes equations in a porous medium that evolves over time. The evolution is a priori given. At the interface of the pore space and the solid part, we prescribe an inhomogeneous Dirichlet boundary condition, which enables a no-slip boundary condition at the evolving boundary. We pass rigorously to the homogenisation limit employing the two-scale
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Isochronous global center of linear plus homogeneous polynomial systems and cubic systems J. Differ. Equ. (IF 2.4) Pub Date : 2024-03-13 Yingtao Li, Shaowen Shi, Jun Zhang
We prove that any planar polynomial differential system with linear plus homogeneous nonlinearities has no isochronous global centers and obtain all cubic polynomial differential systems having an isochronous global center.
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New class of perturbations for nonuniform exponential dichotomy roughness J. Differ. Equ. (IF 2.4) Pub Date : 2024-03-13 Manuel Pinto, Felipe Poblete, Yonghui Xia
We investigate the roughness of nonuniform exponential dichotomies in Banach spaces subject to a new class of small linear time variable perturbations that satisfy an integral inequality which can benefit from a smallness integrability condition. We establish the continuous dependence of constants in terms of a dichotomy notion. Our proofs introduce a new development based on integral inequalities
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Stability of strong viscous shock wave under periodic perturbation for 1-D isentropic Navier-Stokes system in the half space J. Differ. Equ. (IF 2.4) Pub Date : 2024-03-08 Lin Chang, Lin He, Jin Ma
In this paper, a viscous shock wave under space-periodic perturbation of 1-D isentropic Navier-Stokes system in the half space is investigated. It is shown that if the initial periodic perturbation around the viscous shock wave is small, then the solution time asymptotically tends to a viscous shock wave with a shift partially determined by the periodic oscillations. Moreover the strength of shock
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Inverse spectral problem for a third-order differential operator on a finite interval J. Differ. Equ. (IF 2.4) Pub Date : 2024-03-08 V.A. Zolotarev
Inverse spectral problem for a self-adjoint differential operator, which is the sum of the operator of the third derivative on a finite interval and of the operator of multiplication by a real function (potential), is solved. Closed system of integral linear equations is obtained. Via solution to this system, the potential is calculated. It is shown that the main parameters of the obtained system of
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On counterexamples to unique continuation for critically singular wave equations J. Differ. Equ. (IF 2.4) Pub Date : 2024-03-08 Simon Guisset, Arick Shao
We consider wave equations with a critically singular potential diverging as an inverse square at a hypersurface . Our aim is to construct counterexamples to unique continuation from for this equation, provided there exists a family of null geodesics trapped near . This extends the classical geometric optics construction of Alinhac-Baouendi (i) to linear differential operators with singular coefficients
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Measurable weighted shadowing for random dynamical systems on Banach spaces J. Differ. Equ. (IF 2.4) Pub Date : 2024-03-07 Davor Dragičević, Weinian Zhang, Linfeng Zhou
In this paper we study the unique weighted measurable shadowing property for weighted pseudo-orbits of random systems on Banach spaces with the property that linear part of random system admits a tempered exponential dichotomy. We also prove for linear random systems that the tempered exponential dichotomy is necessary for the unique weighted measurable shadowing property to hold.
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Towards weak KAM theory at relative equilibrium J. Differ. Equ. (IF 2.4) Pub Date : 2024-03-07 Xun Niu, Shuguan Ji, Yong Li
We study the weak KAM theory for finite co-dimensional Hamiltonian with relative equilibrium. On the one hand, for the Tonelli (strictly convex, superlinear) finite co-dimensional Hamiltonian, we utilize Evans' approximate variational principle and show that the Hamilton-Jacobi equation with relative equilibrium has a weak KAM solution. It as a generating function can transform the original Hamiltonian
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A free boundary singular transport equation as a formal limit of a discrete dynamical system J. Differ. Equ. (IF 2.4) Pub Date : 2024-03-06 Giovanni Bellettini, Alessandro Betti, Maurizio Paolini
We study the continuous version of a hyperbolic rescaling of a discrete game, called open mancala. The resulting PDE turns out to be a singular transport equation, with a forcing term taking values in , and discontinuous in the solution itself. We prove existence and uniqueness of a certain formulation of the problem, based on a nonlocal equation satisfied by the free boundary dividing the region where
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Analysis of a Poisson–Nernst–Planck–Fermi system for charge transport in ion channels J. Differ. Equ. (IF 2.4) Pub Date : 2024-03-06 Ansgar Jüngel, Annamaria Massimini
A modified Poisson–Nernst–Planck system in a bounded domain with mixed Dirichlet–Neumann boundary conditions is analyzed. It describes the concentrations of ions immersed in a polar solvent and the correlated electric potential due to the ion–solvent interaction. The concentrations solve cross-diffusion equations, which are thermodynamically consistent. The considered mixture is saturated, meaning
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The Landau equation with moderate soft potentials: An approach using ε-Poincaré inequality and Lorentz spaces J. Differ. Equ. (IF 2.4) Pub Date : 2024-03-06 R. Alonso, V. Bagland, B. Lods
This document presents an elementary approach using -Poincaré inequality to prove generation of -bounds, , for the homogeneous Landau equation with moderate soft potentials . The critical case uses an interpolation approach in the realm of Lorentz spaces and entropy. Alternatively, a direct approach using the Hardy-Littlewood-Sobolev (HLS) inequality and entropy is also presented. On this basis, the
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Note on a nonlinear coupled 4th-order parabolic problem J. Differ. Equ. (IF 2.4) Pub Date : 2024-03-06 Fengjie Li, Ping Li
This paper deals with the coupled fourth-order parabolic equations, subject to Dirichlet or Navier boundary conditions. We combine the generalized potential well method, the concave method, with the auxiliary methods to classify the initial energy about the existence of blow-up solutions and global solutions. Moreover, the decay estimate of global solutions and the bounds of blow-up time and rate are
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The maximum number of centers for planar polynomial Kolmogorov differential systems J. Differ. Equ. (IF 2.4) Pub Date : 2024-03-06 Hongjin He, Dongmei Xiao
The maximum number of centers is an open problem proposed by Gasull for planar polynomial differential systems of degree with . In this paper we study the problem for planar polynomial Kolmogorov differential systems of degree , prove that the maximum number of centers is exactly seven for planar quartic polynomial Kolmogorov differential systems, and give the upper and lower bound for the maximum
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Structural stability of subsonic steady-states to the bipolar Euler-Poisson equations with degenerate boundary J. Differ. Equ. (IF 2.4) Pub Date : 2024-03-06 Shiqiang Zhao, Ming Mei, Kaijun Zhang
This paper concerns the structural stability of subsonic steady-states to the bipolar Euler-Poisson equations under small perturbation of doping profiles. Here, the electron density is imposed with degenerate sonic boundary and considered in interiorly subsonic case, while the hole density is considered in fully subsonic case. Unlike the unipolar model, we show that the structural stability in bipolar
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Sharp well-posedness for the Cauchy problem of the two dimensional quadratic nonlinear Schrödinger equation with angular regularity J. Differ. Equ. (IF 2.4) Pub Date : 2024-03-06 Hiroyuki Hirayama, Shinya Kinoshita, Mamoru Okamoto
This paper is concerned with the Cauchy problem of the quadratic nonlinear Schrödinger equation in with the nonlinearity where and low regularity initial data. If , the ill-posedness result in the Sobolev space is known. We will prove the well-posedness in for by assuming some angular regularity on initial data. The key tools are the modified Fourier restriction norm and the convolution estimate on
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Wong-Zakai approximations and random attractors for stochastic p-Laplacian lattice systems J. Differ. Equ. (IF 2.4) Pub Date : 2024-03-04 Xuping Zhang, Rong Liang
This paper is concerned with the pathwise dynamics of stochastic -Laplacian lattice systems driven by Wong-Zakai type approximation noises. The existence and uniqueness of pullback random attractor are established for the approximate system with a wide class of nonlinear diffusion term. When the stochastic system is driven by a linear multiplicative noise, we prove the convergence of solutions and
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Long time stability result for d-dimensional nonlinear Schrödinger equation J. Differ. Equ. (IF 2.4) Pub Date : 2024-03-04 Hongzi Cong, Siming Li, Xiaoqing Wu
In this paper, we study the long time dynamical behavior of the solutions for -dimensional nonlinear Schödinger equation with general nonlinearity by using Birkhoff normal form technique and the so-called property in Gevrey space and modified Sobolev space.
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Construction of the free-boundary 3D incompressible Euler flow under limited regularity J. Differ. Equ. (IF 2.4) Pub Date : 2024-03-04 Mustafa Sencer Aydin, Igor Kukavica, Wojciech S. Ożański, Amjad Tuffaha
We consider the three-dimensional Euler equations in a domain with a free boundary with no surface tension. In the Lagrangian setting, we construct a unique local-in-time solution for such that the Rayleigh-Taylor condition holds and in an arbitrarily small neighborhood of the free boundary. We show that the result is optimal in the sense that regularity of the Lagrangian deformation near the free
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Travelling wave solutions for gravity fingering in porous media flows J. Differ. Equ. (IF 2.4) Pub Date : 2024-03-01 K. Mitra, A. Rätz, B. Schweizer
We study an imbibition problem for porous media. When a wetted layer is above a dry medium, gravity leads to the propagation of the water downwards into the medium. In experiments, the occurrence of fingers was observed, a phenomenon that can be described with models that include hysteresis. In the present paper we describe a single finger in a moving frame and set up a free boundary problem to describe
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Concentrated solutions with helical symmetry for the 3D Euler equation and rearrangments J. Differ. Equ. (IF 2.4) Pub Date : 2024-03-01 Daomin Cao, Boquan Fan, Shanfa Lai
In this paper, we study the existence and stability of concentrated traveling-rotating helical vortex for the 3D incompressible Euler equations in an infinite pipe. The solutions are obtained by maximization of the energy over the set of rearrangments of a fixed bounded function with compact support, and tends asymptotically to singular helical vortex filament evolving by the binormal curvature flow
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On weak solutions to the geodesic equation in the presence of curvature bounds J. Differ. Equ. (IF 2.4) Pub Date : 2024-02-29 Moritz Reintjes, Blake Temple
We show that taking account of bounded curvature reduces the threshold regularity of connection coefficients required for existence and uniqueness of solutions to the geodesic equation, to , one derivative below the regularity required if one does not take account of curvature. We prove curvature in gives local existence and curvature in gives uniqueness. Our argument is based on the authors' theory
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Spherically symmetric evolution of self-gravitating massive fields J. Differ. Equ. (IF 2.4) Pub Date : 2024-02-28 Philippe G. LeFloch, Filipe C. Mena, The-Cang Nguyen
We are interested in the global dynamics of a scalar field evolving under its own gravitational field and, in this paper, we study spherically symmetric solutions to Einstein's field equations coupled with a Klein-Gordon equation with quadratic potential. For the initial value problem we establish a global existence theory when initial data are prescribed on a future light cone with vertex at the center
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On special properties of solutions to the Benjamin-Bona-Mahony equation J. Differ. Equ. (IF 2.4) Pub Date : 2024-02-27 Christian Hong, Gustavo Ponce
This work is concerned with the Benjamin-Bona-Mahony equation. This model was deduced as an approximation to the Korteweg-de Vries equation in the description of the unidirectional propagation of long waves. Our goal here is to study unique continuation and regularity properties on solutions to the associated initial value problem and initial periodic boundary value problems.
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A note to the global solvability of a chemotaxis-Navier-Stokes system with density-suppressed motility J. Differ. Equ. (IF 2.4) Pub Date : 2024-02-27 Zhaoyin Xiang, Ju Zhou
In this note, we investigate the following incompressible chemotaxis-Navier-Stokes system with density-suppressed motility in a bounded convex domain with smooth boundary under the no-flux boundary conditions for , and the Dirichlet boundary condition for . We showed that for general (large) regular initial data, this system admits a global classical solution, which is uniformly bounded with respect
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Global existence, boundedness and asymptotic behavior of classical solutions to a fully parabolic two-species chemotaxis-competition model with singular sensitivity J. Differ. Equ. (IF 2.4) Pub Date : 2024-02-27 Weiyi Zhang, Zuhan Liu
This paper deals with the following parabolic-parabolic-parabolic chemotaxis system with singular sensitivity and Lotka-Volterra competition kinetics where is a bounded smooth convex domain, and the parameters and are positive constants. It is shown that the system possesses globally bounded classical solutions under the following conditions or . Moreover, if , we obtain the uniformly lower bound for
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Global solutions and relaxation limit to the Cauchy problem of a hydrodynamic model for semiconductors J. Differ. Equ. (IF 2.4) Pub Date : 2024-02-27 Yun-guang Lu
In this paper, we study the Cauchy problem for the one-dimensional Euler-Poisson (or hydrodynamic) model for semiconductors, where the energy equation is replaced by a pressure-density relation. First, the existence of global entropy solutions is proved by using the vanishing artificial viscosity method, where, a special flux approximate is introduced to ensure the uniform boundedness of the electric
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Stability and exponential decay for the compressible Oldroyd-B model with non-small coupling parameter J. Differ. Equ. (IF 2.4) Pub Date : 2024-02-26 Chengjun Guo, Xiaoping Zhai, Shunhang Zhang
This paper presents the global stability and the large-time behavior of solutions to the compressible Oldroyd-B model in a periodic domain. Moreover, we show that the -norm of the solutions decays exponentially in time. It is worth pointing out that the coupling parameter is not necessary to be small enough in our result.
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Localization for general Helmholtz J. Differ. Equ. (IF 2.4) Pub Date : 2024-02-26 Xinyu Cheng, Dong Li, Wen Yang
In , Guan, Murugan and Wei established the equivalence of the classical Helmholtz equation with a “fractional Helmholtz” equation in which the Laplacian operator is replaced by the nonlocal fractional Laplacian operator. More general equivalence results are obtained for symbols which are complete Bernstein and satisfy additional regularity conditions. In this work we introduce a novel and general set-up
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Zero-mass gauged Schrödinger equations with supercritical exponential growth J. Differ. Equ. (IF 2.4) Pub Date : 2024-02-23 Liejun Shen
We study the following gauged nonlinear Schrödinger equation where , , and possesses the supercritical exponential growth in the Trudinger-Moser sense at infinity. Via introducing a new type of Trudinger-Moser inequality in a suitable work space here, we shall exploit the general minimax principle and elliptic regular result to investigate the existence of mountain-pass type solutions for the equation
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The Landau and non-cutoff Boltzmann equations in union of cubes J. Differ. Equ. (IF 2.4) Pub Date : 2024-02-23 Dingqun Deng
The existence and stability of collisional kinetic equations, especially non-cutoff Boltzmann equation, in a bounded domain with physical boundary condition is a longstanding open problem. This work proves the global stability of the Landau equation and non-cutoff Boltzmann equation in union of cubes with the specular reflection boundary condition when an initial datum is near Maxwellian. Moreover
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Optimising the carrying capacity in logistic diffusive models: Some qualitative results J. Differ. Equ. (IF 2.4) Pub Date : 2024-02-23 Idriss Mazari-Fouquer
We revisit the problem of optimising (either maximising or minimising) the total biomass or wider classes of criteria in logistic-diffusive models. Since , a lot of effort has been devoted to the qualitative understanding of the following question: how should one spread resources in order to maximise or minimise the total biomass? This question was studied in detail, mostly in situations where the
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A reiterated homogenization problem for the p-Laplacian equation in corrugated thin domains J. Differ. Equ. (IF 2.4) Pub Date : 2024-02-22 Jean Carlos Nakasato, Marcone Corrêa Pereira
In this paper, we study the asymptotic behavior of the solutions of the -Laplacian equation with mixed homogeneous Neumann-Dirichlet boundary conditions. It is posed in a two-dimensional rough thin domain with two different composites periodically distributed. Each composite has its own periodicity and roughness order. Here, we obtain distinct homogenized limit equations which will depend on the relationship
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Global well-posedness for the 2D Euler-Boussinesq-Bénard equations with critical dissipation J. Differ. Equ. (IF 2.4) Pub Date : 2024-02-22 Zhuan Ye
This present paper is dedicated to the study of the Cauchy problem of the two-dimensional Euler-Boussinesq-Bénard equations which couple the incompressible Euler equations for the velocity and a transport equation with critical dissipation for the temperature. We show that there is a global unique solution to this model with Yudovich's type data. This settles the global regularity problem which was
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Example of Turing's instability by equal diffusion J. Differ. Equ. (IF 2.4) Pub Date : 2024-02-22 Hirokazu Ninomiya
In 1952, Turing proposed the mechanism of pattern formation in which a stable equilibrium of some kinetic system is destabilized by diffusion. This mechanism is called Turing's instability, which is one of important mechanisms to organize spatiotemporal patterns. In the case of two-component reaction–diffusion systems, the diffusion coefficients should be different for Turing's instability. Conversely
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Qualitative study of the Selkov model J. Differ. Equ. (IF 2.4) Pub Date : 2024-02-22 Jaume Llibre, Chara Pantazi
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On the unique solvability of radiative transfer equations with polarization J. Differ. Equ. (IF 2.4) Pub Date : 2024-02-22 Vincent Bosboom, Matthias Schlottbom, Felix L. Schwenninger
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Well-posedness of logarithmic spiral vortex sheets J. Differ. Equ. (IF 2.4) Pub Date : 2024-02-22 Tomasz Cieślak, Piotr Kokocki, Wojciech S. Ożański
We consider a family of 2D logarithmic spiral vortex sheets which include the celebrated spirals introduced by Prandtl and by Alexander . We prove that for each such spiral the normal component of the velocity field remains continuous across the spiral. We give sufficient conditions for spiral vortex sheets to be weak solutions of the 2D incompressible Euler equations. Namely, we show that a spiral
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Minimization of the first positive Neumann-Dirichlet eigenvalue for the Camassa-Holm equation with indefinite potential J. Differ. Equ. (IF 2.4) Pub Date : 2024-02-21 Haiyan Zhang, Jijun Ao
The aim of this paper is to obtain the sharp estimate for the lowest positive eigenvalue for the Camassa-Holm equation with the Neumann-Dirichlet boundary conditions, where potential admits to change sign. We first study the optimal lower bound for the smallest positive eigenvalue in the measure differential equations. Then based on the relationship between the minimization problem of the smallest
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Pullback attractors with finite fractal dimension for a semilinear transfer equation with delay in some non-cylindrical domain J. Differ. Equ. (IF 2.4) Pub Date : 2024-02-20 Heraclio López-Lázaro, Marcelo J.D. Nascimento, Carlos R. Takaessu Junior, Vinicius T. Azevedo
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Generalized eigenvalue problem for an interface elliptic equation J. Differ. Equ. (IF 2.4) Pub Date : 2024-02-20 Braulio B.V. Maia, Mónica Molina-Becerra, Cristian Morales-Rodrigo, Antonio Suárez
In this paper we deal with an eigenvalue problem in an interface elliptic equation. We characterize the set of principal eigenvalues as a level set of a concave and regular function. As application, we study a problem arising in population dynamics. In these problems each species lives in a subdomain, and they interact in a common border, which acts as a geographical barrier; but unlike previous results
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BV solutions to a hyperbolic system of balance laws with logistic growth J. Differ. Equ. (IF 2.4) Pub Date : 2024-02-20 Geng Chen, Yanni Zeng
We study BV solutions for a system of hyperbolic balance laws. We show that when initial data have small total variation on and small amplitude, and decay sufficiently fast to a constant equilibrium state as , a Cauchy problem (with generic data) has a unique admissible BV solution defined globally in time. Here the solution is admissible in the sense that its shock waves satisfy the Lax entropy condition
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Sharp convex generalizations of stochastic Gronwall inequalities J. Differ. Equ. (IF 2.4) Pub Date : 2024-02-20 Sarah Geiss
We provide generalizations of a class of stochastic Gronwall inequalities that has been studied by von Renesse and Scheutzow (2010), Scheutzow (2013), Xie and Zhang (2020) and Mehri and Scheutzow (2021). This class of stochastic Gronwall inequalities is a useful tool for SDEs.
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Global well-posedness and stability of the 2D Boussinesq equations with partial dissipation near a hydrostatic equilibrium J. Differ. Equ. (IF 2.4) Pub Date : 2024-02-20 Kyungkeun Kang, Jihoon Lee, Dinh Duong Nguyen
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Multi-piece of bubble solutions for a nonlinear critical elliptic equation J. Differ. Equ. (IF 2.4) Pub Date : 2024-02-20 Fan Du, Qiaoqiao Hua, Chunhua Wang, Qingfang Wang
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Long-time asymptotics of the Hunter-Saxton equation on the line J. Differ. Equ. (IF 2.4) Pub Date : 2024-02-19 Luman Ju, Kai Xu, Engui Fan
With -generalization of the Deift-Zhou steepest descent method, we investigate the long-time asymptotics of the solution to the Cauchy problem for the Hunter-Saxton (HS) equation where and is a constant. Via a series of deformations to a Riemann-Hilbert problem associated with the Cauchy problem, we obtain the long-time asymptotic approximations of the solution in two kinds of space-time regions under
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Non-uniform dependence on initial data for the Camassa–Holm equation in Besov spaces: Revisited J. Differ. Equ. (IF 2.4) Pub Date : 2024-02-15 Jinlu Li, Yanghai Yu, Weipeng Zhu
In the paper, we revisit the uniform continuity properties of the data-to-solution map of the Camassa–Holm equation on the real-line case. We show that the data-to-solution map of the Camassa–Holm equation is not uniformly continuous on the initial data in Besov spaces with and , which improves the previous works Himonas et al. (2007) , Li et al. (2020) and Li et al. (2021) . Furthermore, we present
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Induced delay equations J. Differ. Equ. (IF 2.4) Pub Date : 2024-02-15 Luís Barreira, Claudia Valls
For the family of nonautonomous delay equations, we show that the generator of the evolution semigroup obtained from any such equation gives rise to an delay equation on a higher-dimensional space. We call it an . More significantly, we show that this equation can be used to study some important properties of the original dynamics in four main directions: the characterization of the hyperbolicity of
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Functional Volterra Stieltjes integral equations and applications J. Differ. Equ. (IF 2.4) Pub Date : 2024-02-14 R. Grau, C. Lafetá, J.G. Mesquita
In this paper, we introduce a more general class of equations called functional Volterra integral equations involving measures, which encompass many types of equations such as functional Volterra equations, functional Volterra equations with impulses, functional Volterra delta integral equations on time scales, functional fractional differential equations with and without impulses, among others. Also
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A dynamic approach to heterogeneous elastic wires J. Differ. Equ. (IF 2.4) Pub Date : 2024-02-14 Anna Dall'Acqua, Leonie Langer, Fabian Rupp
We consider closed planar curves with fixed length and arbitrary winding number whose elastic energy depends on an additional density variable and a spontaneous curvature. Working with the inclination angle, the associated -gradient flow is a nonlocal quasilinear coupled parabolic system of second order. We show local well-posedness, global existence of solutions, and full convergence of the flow for
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Dirac operators with operator data of Wigner-von Neumann type J. Differ. Equ. (IF 2.4) Pub Date : 2024-02-14 Ethan Gwaltney
We consider half-line Dirac operators with operator data of Wigner-von Neumann type. If the data is a finite linear combination of Wigner-von Neumann functions, we show absence of singular continuous spectrum and provide an explicit set containing all embedded pure points that depends only on the decay and frequencies of the operator data. For infinite sums of Wigner-von Neumann-like terms, we bound
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Finite energy solutions for nonlinear elliptic equations with competing gradient, singular and L1 terms J. Differ. Equ. (IF 2.4) Pub Date : 2024-02-13 Francesco Balducci, Francescantonio Oliva, Francesco Petitta
In this paper we deal with the following boundary value problem in a domain , where , is a positive and continuous function on , and is a continuous function on (possibly blowing up at the origin). We show how the presence of regularizing terms and allows to prove existence of finite energy solutions for nonnegative data only belonging to .
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Inviscid limit for the compressible Navier-Stokes equations with density dependent viscosity J. Differ. Equ. (IF 2.4) Pub Date : 2024-02-12 Luca Bisconti, Matteo Caggio
We consider the compressible Navier-Stokes system describing the motion of a barotropic fluid with density dependent viscosity confined in a three-dimensional bounded domain Ω. We show the convergence of the weak solution to the compressible Navier-Stokes system to the strong solution to the compressible Euler system when the viscosity and the damping coefficients tend to zero.
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Action and periodic orbits of area-preserving diffeomorphisms J. Differ. Equ. (IF 2.4) Pub Date : 2024-02-09 Huadi Qu, Zhihong Xia
We study periodic points for area-preserving maps on surfaces, particularly some global properties related to the action functional. We generalize recent works of Hutchings and Weiler , proving the existence of periodic orbits with certain action values.
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Linear first order differential operators and their Hutchinson invariant sets J. Differ. Equ. (IF 2.4) Pub Date : 2024-02-09 Per Alexandersson, Nils Hemmingsson, Dmitry Novikov, Boris Shapiro, Guillaume Tahar
In this paper, we initiate the study of a new interrelation between linear ordinary differential operators and complex dynamics which we discuss in detail in the simplest case of operators of order 1. Namely, assuming that such an operator has polynomial coefficients, we interpret it as a continuous family of Hutchinson operators acting on the space of positive powers of linear forms. Using this interpretation
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The uniqueness of the slowly uniformly rotating supermassive star for a given total mass J. Differ. Equ. (IF 2.4) Pub Date : 2024-02-09 Yucong Wang
A rotating supermassive star can be modeled by the self-gravitational Euler-Poisson equations for the case that the equation of state is of the form . We prove the uniqueness of the slowly uniformly rotating supermassive star solution which is the steady-state solution of the compressible self-gravitational Euler-Poisson system with a given constant angular velocity and total mass. This solves a problem
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Bifurcation structure of indefinite nonlinear diffusion problem in population genetics J. Differ. Equ. (IF 2.4) Pub Date : 2024-02-08 Kimie Nakashima, Tohru Tsujikawa
We study positive stationary solutions for the following Neumann problem in one-dimension space arising from population genetics: where changes sign once in and is a positive parameter. This equation has a stationary positive solution , where has zeros in . We denote this solution by an -solution . We show that the -solution branch bifurcates from the trivial solution and the -solution branch does