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Asymptotic behavior of the 3D incompressible Navier–Stokes equations with damping Nonlinear Anal. (IF 1.4) Pub Date : 2024-04-12 Fuxian Peng, Xueting Jin, Huan Yu
In this paper, we consider the 3D incompressible Navier–Stokes equations with damping term First, by using a different and simple method from Cai and Lei (2010), Jia et al. (2011), Jiang (2012) and Yu and Zheng (2019), for any we prove that the weak solutions decay to zero in as time tends to infinity; for any we derive optimal decay rates of the -norm of the solutions. Second, we obtain the decay
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Geometric inequalities and their stabilities for modified quermassintegrals in hyperbolic space Nonlinear Anal. (IF 1.4) Pub Date : 2024-04-09 Chaoqun Gao, Rong Zhou
In this paper, we first consider the curve case of Hu-Li-Wei’s flow for shifted principal curvatures of h-convex hypersurfaces in proposed in Hu et al. (2022). We prove that if the initial closed curve is smooth and strictly h-convex, then the solution exists for all time and preserves strict h-convexity along the flow. Moreover, the evolving curve converges smoothly and exponentially to a geodesic
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Besov regularity and optimal estimation of bilevel variational inequality problems on cylindrical domains and their applications Nonlinear Anal. (IF 1.4) Pub Date : 2024-04-08 Wenbing Wu
In this paper, we provide a unified approach to investigating Besov regularity and the optimum estimate for bilevel variational inequality problems on cylindrical domains. This method is effective even with limited summary data available, demonstrating its practicality. The novelty of our approach resides in the treatment of subquadratic growth conditions associated with the gradient variable. We extend
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The cubic nonlinear fractional Schrödinger equation on the half-line Nonlinear Anal. (IF 1.4) Pub Date : 2024-04-04 Márcio Cavalcante, Gerardo Huaroto
We study the cubic nonlinear fractional Schrödinger equation with Lévy indices posed on the half-line. More precisely, we define the notion of a solution for this model and we obtain a result of local-well-posedness almost sharp in the sense of index of regularity required for the solutions with respect for known results on the full real line . Also, we prove for the same model that the solution of
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Derivation and well-posedness for asymptotic models of cold plasmas Nonlinear Anal. (IF 1.4) Pub Date : 2024-04-02 Diego Alonso-Orán, Angel Durán, Rafael Granero-Belinchón
In this paper we derive three new asymptotic models for a hyperbolic–hyperbolic–elliptic system of PDEs describing the motion of a collision-free plasma in a magnetic field. The first of these models takes the form of a non-linear and non-local Boussinesq system (for the ionic density and velocity) while the second is a non-local wave equation (for the ionic density). Moreover, we derive a unidirectional
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High order asymptotic inequalities for some dissipative systems Nonlinear Anal. (IF 1.4) Pub Date : 2024-04-02 P. Braz e Silva, R.H. Guterres, C.F. Perusato, P.R. Zingano
We obtain some important fundamental inequalities concerning the long time behavior of high order derivatives for solutions of some dissipative systems in terms of their algebraic decay. Some of these inequalities have not been observed in the literature even for the fundamental Navier–Stokes equations. To illustrate this new approach, we derive bounds for the asymmetric incompressible fluids equations
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Analysis of a two phase flow model of biofilm spread Nonlinear Anal. (IF 1.4) Pub Date : 2024-03-20 Ana Carpio, Gema Duro
We consider a quasi-stationary problem describing the status of velocities, pressures and chemicals affecting cell behavior within a biofilm. The model couples stationary transport equations and compressible Stokes systems with convection–reaction–diffusion equations. We establish existence, uniqueness and stability of solutions of the different submodels involved and then obtain well posedness results
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Cherrier–Escobar problem for the elliptic Schrödinger-to-Neumann map Nonlinear Anal. (IF 1.4) Pub Date : 2024-03-20 Mohammed Aldawood, Cheikh Birahim Ndiaye
In this paper, we study a Cherrier–Escobar problem for the extended problem corresponding to the elliptic Schrödinger-to-Neumann map on a compact 3-dimensional Riemannian manifold with boundary. Using the algebraic topological argument of Bahri and Coron (1988), we show solvability under the assumption that the extended problem corresponding to the elliptic Schrödinger-to-Neumann map has a positive
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Asymptotic motions converging to arbitrary dynamics for time-dependent Hamiltonians Nonlinear Anal. (IF 1.4) Pub Date : 2024-03-13 Donato Scarcella
Dynamical systems subject to perturbations that decay over time are relevant in the description of many physical models, e.g. when considering the effect of a laser pulse on a molecule, in epidemiological studies, as well as in celestial mechanics. For this reason, we consider a Hamiltonian dynamical system having an invariant torus supporting arbitrary dynamics, and we study its evolution under a
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Hadamard’s inequality in the mean Nonlinear Anal. (IF 1.4) Pub Date : 2024-03-13 Jonathan Bevan, Martin Kružík, Jan Valdman
Let be a Lipschitz domain in and let . We investigate conditions under which the functional obeys for all , an inequality that we refer to as Hadamard-in-the-mean, or (HIM). We prove that there are piecewise constant such that (HIM) holds and is strictly stronger than the best possible inequality that can be derived using the Hadamard inequality alone. When takes just two values, we find that (HIM)
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Instability of homogeneous steady states in chemotaxis systems with flux limitation Nonlinear Anal. (IF 1.4) Pub Date : 2024-03-10 Xuan Mao, Yuxiang Li
This paper is concerned with chemotaxis systems with flux limitation , for some , subjected to homogeneous Neumann boundary conditions in a bounded domain . Due to Winkler [M.Winkler, Indiana Univ. Math. J., 71 (2022), 1437–1465], the systems with radial assumptions admit a critical exponent for finite-time blowup. We further consider the radial solutions blowing up under supercritical settings and
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Narrow operators on [formula omitted]-complete lattice-normed spaces Nonlinear Anal. (IF 1.4) Pub Date : 2024-03-07 Nonna Dzhusoeva, Eleonora Grishenko, Marat Pliev, Fedor Sukochev
We extend some of main results of Abasov et al., 2016, Fotiy et al., (2020), Mykhaylyuk et al., (2015), Pliev and Fang, (2017), Pliev and Popov, (2014) to the setting of orthogonally additive operators on lattice-normed spaces. We introduce a new class of -complete lattice-normed spaces which strictly includes a class of Banach–Kantorovich spaces. The first main result of the paper asserts that every
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Periodic partitions with minimal perimeter Nonlinear Anal. (IF 1.4) Pub Date : 2024-03-06 Annalisa Cesaroni, Matteo Novaga
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Vanishing capillarity–viscosity limit of the incompressible Navier–Stokes–Korteweg equations with slip boundary condition Nonlinear Anal. (IF 1.4) Pub Date : 2024-03-05 Pingping Wang, Zhipeng Zhang
In this paper, we investigate the vanishing capillarity–viscosity limit of the incompressible Navier–Stokes–Korteweg (NSK) equations in a three-dimensional horizontally periodic strip domain, in which the velocity of the fluid is supplemented with slip boundary condition and the gradient of density with Dirichlet boundary condition on the boundary. We prove that there exists an positive constant independent
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Fractional Hardy–Rellich inequalities via integration by parts Nonlinear Anal. (IF 1.4) Pub Date : 2024-03-05 Nicola De Nitti, Sidy Moctar Djitte
We prove a fractional Hardy–Rellich inequality with an explicit constant in bounded domains of class . The strategy of the proof generalizes an approach pioneered by E. Mitidieri (, 2000) by relying on a Pohozaev-type identity.
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On the global and singular dynamics of the 2D cubic nonlinear Schrödinger equation on cylinders Nonlinear Anal. (IF 1.4) Pub Date : 2024-02-28 Adán J. Corcho, Mahendra Panthee
We consider the Cauchy problem associated to the focusing cubic nonlinear Schrödinger equation posed on a two dimensional cylindrical domain . We prove that localized transverse perturbations of an especial one-parameter family of bound states solutions , can be extended globally in time. On the other hand, we establish the existence of solution in the energy space , with non-critical mass, that blows-up
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Quasilinear Lane–Emden type systems with sub-natural growth terms Nonlinear Anal. (IF 1.4) Pub Date : 2024-02-26 Estevan Luiz da Silva, João Marcos do Ó
Global pointwise estimates are obtained for quasilinear Lane–Emden-type systems involving measures in the “sublinear growth” rate. We give necessary and sufficient conditions for existence expressed in terms of Wolff’s potential. Our approach is based on recent advances due to Kilpeläinen and Malý in the potential theory. This method enables us to treat several problems, such as equations involving
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Asymptotic decay of solutions for sublinear fractional Choquard equations Nonlinear Anal. (IF 1.4) Pub Date : 2024-02-24 M, a, r, c, o, , G, a, l, l, o
Goal of this paper is to study the asymptotic behaviour of the solutions of the following doubly nonlocal equation where , , , , denotes the Riesz potential and is a general nonlinearity with a sublinear growth in the origin. The found decay is of polynomial type, with a rate possibly slower than . The result is new even for homogeneous functions , , and it complements the decays obtained in the linear
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Growth of Sobolev norms and strong convergence for the discrete nonlinear Schrödinger equation Nonlinear Anal. (IF 1.4) Pub Date : 2024-02-20 Q, u, e, n, t, i, n, , C, h, a, u, l, e, u, r
We show the strong convergence in arbitrary Sobolev norms of solutions of the discrete nonlinear Schrödinger on an infinite lattice towards those of the nonlinear Schrödinger equation on the whole space. We restrict our attention to the one and two-dimensional case, with a set of parameters which implies global well-posedness for the continuous equation. Our proof relies on the use of bilinear estimates
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About the general chain rule for functions of bounded variation Nonlinear Anal. (IF 1.4) Pub Date : 2024-02-19 Camillo Brena, Nicola Gigli
We give an alternative proof of the general chain rule for functions of bounded variation (Ambrosio and Maso, 1990), which allows to compute the distributional differential of , where and . In our argument we build on top of recently established links between “closability of certain differentiation operators” and “differentiability of Lipschitz functions in related directions” (Alberti et al., 2023):
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Higher regularity for minimizers of very degenerate convex integrals Nonlinear Anal. (IF 1.4) Pub Date : 2024-02-19 A, n, t, o, n, i, o, , G, i, u, s, e, p, p, e, , G, r, i, m, a, l, d, i
In this paper, we consider minimizers of integral functionals of the type for , where , with , is a possibly vector-valued function. Here, is the associated norm of a bounded, symmetric and coercive bilinear form on . We prove that is continuous in , for any continuous function vanishing on .
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Global behavior of the solutions to nonlinear wave equations with combined power-type nonlinearities with variable coefficients Nonlinear Anal. (IF 1.4) Pub Date : 2024-02-09 M. Dimova, N. Kolkovska, N. Kutev
In this paper we study the initial boundary value problem for the nonlinear wave equation with combined power-type nonlinearities with variable coefficients. Existence and uniqueness of local weak solutions are proved. The global behavior of the solutions with non-positive and sub-critical energy is completely investigated. The threshold between global existence and finite time blow up is found. For
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Global solution of nonlinear Heat equation with solutions in a Hilbert Manifold Nonlinear Anal. (IF 1.4) Pub Date : 2024-02-09 Z. Brzeźniak, J. Hussain
The objective of this paper is to deal with the deterministic problem consisting of non-linear heat equation of gradient type. The evolution equation emerges as projecting the Laplace operator with Dirichlet boundary conditions and polynomial nonlinearity of degree , onto the tangent space of a sphere in a Hilbert space . We are going to deal with questions of the existence and the uniqueness of a
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Weighted Hessian estimates in Orlicz spaces for nondivergence elliptic operators with certain potentials Nonlinear Anal. (IF 1.4) Pub Date : 2024-02-09 Mikyoung Lee, Yoonjung Lee
We prove interior weighted Hessian estimates in Orlicz spaces for nondivergence type elliptic equations with a lower order term which involves a nonnegative potential satisfying a reverse Hölder type condition.
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Asymptotics of solutions to the periodic problem for the nonlinear damped wave equation with convective nonlinearity Nonlinear Anal. (IF 1.4) Pub Date : 2024-02-09 Rafael Carreño-Bolaños, Pavel I. Naumkin
We consider the periodic problem for the nonlinear damped wave equation with pumping and convective nonlinearity where We study the solutions, which satisfy the periodic boundary conditions for all and with the - periodic initial data and Our aim in the present paper is to find the large time asymptotics for solutions to the periodic problem for the nonlinear damped wave equation (1.1) carefully studying
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Continuity up to the boundary for obstacle problems to porous medium type equations Nonlinear Anal. (IF 1.4) Pub Date : 2024-02-08 Kristian Moring, Leah Schätzler
We show that signed weak solutions to obstacle problems for porous medium type equations with Cauchy–Dirichlet boundary data are continuous up to the parabolic boundary, provided that the obstacle and boundary data are continuous. This result seems to be new even for signed solutions to the (obstacle free) Cauchy–Dirichlet problem to the singular porous medium equation, which is retrieved as a special
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Variational competition between the full Hessian and its determinant for convex functions Nonlinear Anal. (IF 1.4) Pub Date : 2024-02-08 Peter Gladbach, Heiner Olbermann
We prove upper and lower bounds for a variational functional for convex functions satisfying certain boundary conditions on a sector of the unit ball in two dimensions. The functional contains two terms: The full Hessian and its determinant, where the former is treated as a small perturbation in the space and the latter as the leading-order term, in the negative Sobolev space . We point out how this
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Smoothing and Strichartz estimates for degenerate Schrödinger-type equations Nonlinear Anal. (IF 1.4) Pub Date : 2024-02-07 Serena Federico, Michael Ruzhansky
In this paper we focus on the validity of some fundamental estimates for time-degenerate Schrödinger-type operators. On the one hand we derive global homogeneous smoothing estimates for operators of any order by means of suitable comparison principles (that we shall obtain here). On the other hand, we prove weighted Strichartz-type estimates for time-degenerate Schrödinger operators and apply them
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The Brunn–Minkowski inequality implies the CD condition in weighted Riemannian manifolds Nonlinear Anal. (IF 1.4) Pub Date : 2024-02-06 Mattia Magnabosco, Lorenzo Portinale, Tommaso Rossi
The curvature dimension condition , pioneered by Sturm and Lott–Villani in Sturm (2006a); Sturm (2006b); Lott and Villani (2009), is a synthetic notion of having curvature bounded below and dimension bounded above, in the non-smooth setting. This condition implies a suitable generalization of the Brunn–Minkowski inequality, denoted . In this paper, we address the converse implication in the setting
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The impact of intrinsic scaling on the rate of extinction for anisotropic non-Newtonian fast diffusion Nonlinear Anal. (IF 1.4) Pub Date : 2024-02-03 Simone Ciani, Eurica Henriques, Igor I. Skrypnik
We study the decay towards the extinction that pertains to local weak solutions to fully anisotropic equations whose prototype is Their rates of extinction are evaluated by means of several integral Harnack-type inequalities which constitute the core of our analysis and that are obtained for anisotropic operators having full quasilinear structure. Different decays are obtained when considering different
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Stability of a coupled wave-Klein–Gordon system with non-compactly supported initial data Nonlinear Anal. (IF 1.4) Pub Date : 2024-02-02 Q, i, a, n, , Z, h, a, n, g
In this paper we study global nonlinear stability for a system of semilinear wave and Klein–Gordon equations with quadratic nonlinearities. We consider nonlinearities of the type of wave-Klein–Gordon interactions where there are no derivatives on the wave component. The initial data are assumed to have a suitable polynomial decay at infinity, but are not necessarily compactly supported. We prove small
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Uniqueness theorem for negative solutions of fully nonlinear elliptic equations in a ball Nonlinear Anal. (IF 1.4) Pub Date : 2024-01-30 Z, h, e, n, g, h, u, a, n, , G, a, o
In this paper, we prove the uniqueness of negative radial solution to a Dirichlet problem of -Hessian equation in a finite ball of for . Our proof is based on a Pohozaev identity and the monotone separation techniques.
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On the uniqueness of solutions to the isotropic Lp dual Minkowski problem Nonlinear Anal. (IF 1.4) Pub Date : 2024-01-22 Yingxiang Hu, Mohammad N. Ivaki
We prove that the unit sphere is the only smooth, strictly convex solution to the isotropic Lp dual Minkowski problem hp−1|Dh|n+1−qK=1, provided (p,q)∈(−n−1,−1]×[n,n+1).
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Existence analysis of a cross-diffusion system with nonlinear Robin boundary conditions for vesicle transport in neurites Nonlinear Anal. (IF 1.4) Pub Date : 2024-01-22 Markus Fellner, Ansgar Jüngel
A one-dimensional cross-diffusion system modeling the transport of vesicles in neurites is analyzed. The equations are coupled via nonlinear Robin boundary conditions to ordinary differential equations for the number of vesicles in the reservoirs in the cell body and the growth cone at the end of the neurite. The existence of bounded weak solutions is proved by using the boundedness-by-entropy method
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Global existence of solutions in some chemotaxis systems with sub-logistic source under nonlinear Neumann boundary conditions in 2d Nonlinear Anal. (IF 1.4) Pub Date : 2024-01-25 Minh Le
This paper deals with classical solutions to the chemotaxis system with sub-logistic sources, ru−μu2lnp(u+e), where r,p≥0 and μ>0 under nonlinear Neumann boundary condition in a smooth bounded domain Ω⊂R2. It is shown that if p<1 then solutions exist globally and remain bounded in time. Our proof relies on several techniques, including parabolic regularity in Sobolev spaces, variational arguments,
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A nonlinear damped transmission problem as limit of wave equations with concentrating nonlinear terms away from the boundary Nonlinear Anal. (IF 1.4) Pub Date : 2024-01-19 Ángela Jiménez-Casas, Aníbal Rodríguez-Bernal
In this paper we study an initial and boundary value problem for damped wave equations with nonlinear singular terms concentrating away from the boundary of the domain, on an interior neighbourhood of a hyper-surface M that collapses to M as ɛ goes to zero. We describe the conditions for well posedness of both the approximating and limit problems, as well as the convergence, at the singular limit,
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Stationary solutions and large time asymptotics to a cross-diffusion-Cahn–Hilliard system Nonlinear Anal. (IF 1.4) Pub Date : 2024-01-18 Jean Cauvin-Vila, Virginie Ehrlacher, Greta Marino, Jan-Frederik Pietschmann
We study some properties of a multi-species degenerate Ginzburg–Landau energy and its relation to a cross-diffusion Cahn–Hilliard system. The model is motivated by multicomponent mixtures where cross-diffusion effects between the different species are taken into account, and where only one species does separate from the others. Using a comparison argument, we obtain strict bounds on the minimizers
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A new norm on BLO, matters of approximability and duality Nonlinear Anal. (IF 1.4) Pub Date : 2024-01-18 Francesca Angrisani
In this paper, we obtain an alternative expression for the distance of a function in BLO to the subspace L∞. The distance is the one induced by choosing a new “norm” on BLO, equivalent to the usual one and that has the advantage of making explicitly and exactly computable the distance to L∞. We address the issue of approximability by truncation as it is not obvious even in the closure of L∞ in BLO
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Robust nonlocal trace spaces and Neumann problems Nonlinear Anal. (IF 1.4) Pub Date : 2024-01-05 Florian Grube, Thorben Hensiek
We prove trace and extension results for fractional Sobolev spaces of order s∈(0,1). These spaces are used in the study of nonlocal Dirichlet and Neumann problems on bounded domains. The results are robust in the sense that the continuity of the trace and extension operators is uniform as s approaches 1 and our trace spaces converge to H1/2(∂Ω). We apply these results in order to study the convergence
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Asymptotic stability of solitary waves for the 1D near-cubic non-linear Schrödinger equation in the absence of internal modes Nonlinear Anal. (IF 1.4) Pub Date : 2024-01-05 Guillaume Rialland
We consider perturbations of the one-dimensional cubic Schrödinger equation, under the form i∂tψ+∂x2ψ+|ψ|2ψ−g(|ψ|2)ψ=0. Under hypotheses on the function g that can be easily verified in some cases, we show that the linearized problem around a solitary wave does not have internal mode (nor resonance) and we prove the asymptotic stability of these solitary waves, for small frequencies.
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Evolution of graphs in hyperbolic space by their Gauss curvature Nonlinear Anal. (IF 1.4) Pub Date : 2024-01-06 Shujing Pan, Yong Wei
In this paper, we consider the α-Gauss curvature flow for complete convex graphs over horosphere in the hyperbolic space. We show that for all positive power α>0, if the initial hypersurface is smooth, complete non-compact uniformly convex graph over Rn and bounded by two horospheres, then the solution of the flow exists for all time. Moreover, the evolution of horospheres act as barriers along the
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Controlling a generalized Fokker–Planck equation via inputs with nonlocal action Nonlinear Anal. (IF 1.4) Pub Date : 2024-01-03 Ştefana-Lucia Aniţa
This paper concerns an optimal control problem (P) related to a generalized Fokker–Planck equation. Basic properties of the solutions to the generalized FP equation are derived via a semigroup approach in the space H−1(Rd). Problem (P) is proven to be deeply related to a stochastic optimal control problem (PS) for a McKean–Vlasov equation. The existence of an optimal control is obtained for the deterministic
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Spatial decay properties for a model in shear flows posed on the cylinder Nonlinear Anal. (IF 1.4) Pub Date : 2023-12-28 Ricardo A. Pastrán, Oscar Riaño
We study spatial decay properties for solutions of the Pelinovski–Stepanyants equation posed on the cylinder. We establish the maximum polynomial decay admissible for solutions of such a model. It is verified that the equation on the cylinder propagates polynomial weights with different restrictions than the model set in R2. For example, a local well-posedness theory is deduced which contains the line
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On the convergence of the Willmore flow with Dirichlet boundary conditions Nonlinear Anal. (IF 1.4) Pub Date : 2023-12-27 Manuel Schlierf
Very little is yet known regarding the Willmore flow of surfaces with Dirichlet boundary conditions. We consider surfaces with a rotational symmetry as initial data and prove a global existence and convergence result for solutions of the Willmore flow with initial data below an explicit, sharp energy threshold. Strikingly, this threshold depends on the prescribed boundary conditions — it can even be
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A characterization of BV and Sobolev functions via nonlocal functionals in metric spaces Nonlinear Anal. (IF 1.4) Pub Date : 2023-12-28 Panu Lahti, Andrea Pinamonti, Xiaodan Zhou
We study a characterization of BV and Sobolev functions via nonlocal functionals in metric spaces equipped with a doubling measure and supporting a Poincaré inequality. Compared with previous works, we consider more general functionals. We also give a counterexample in the case p=1 demonstrating that, unlike in Euclidean spaces, in metric measure spaces the limit of the nonlocal functionals is only
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Positive solutions to the planar logarithmic Choquard equation with exponential nonlinearity Nonlinear Anal. (IF 1.4) Pub Date : 2023-12-29 Daniele Cassani, Lele Du, Zhisu Liu
In this paper we study the following nonlinear Choquard equation −Δu+u=ln1|x|∗F(u)f(u),inR2,where f∈C1(R,R) and F is the primitive of the nonlinearity f vanishing at zero. We use an asymptotic approximation approach to establish the existence of positive solutions to the above problem in the standard Sobolev space H1(R2). We give a new proof and at the same time extend part of the results established
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Almost minimizers to a transmission problem for (p,q)-Laplacian Nonlinear Anal. (IF 1.4) Pub Date : 2023-12-22 Sunghan Kim, Henrik Shahgholian
This paper concerns almost minimizers of the functional J(v,Ω)=∫Ω|Dv+|p+|Dv−|qdx,where 1
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A log-weighted Moser inequality on the plane Nonlinear Anal. (IF 1.4) Pub Date : 2023-12-22 C. Tarsi
We establish a sharp Moser type inequality with logarithmic weight in the nonradial mass-weighted Sobolev spaces, on the whole plane R2. We identify the sharp threshold for the uniform boundedness of the weighted Moser functional, which is still given by 4π: further, we prove the validity of the inequality also at the limiting sharp value 4π. Even if the increasing nature of the log weight prevents
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Relative Morse index and multiple solutions for a non-periodic Dirac equation with external fields Nonlinear Anal. (IF 1.4) Pub Date : 2023-12-22 Yuan Shan
This paper is concerned with the stationary solutions of the Dirac equation −i∑k=13αk∂ku+aβu+ωu+V(x)u=Gu(x,u),where G is asymptotically quadratic and is not assumed to be C2. We present a new approach to construct an index theory for the associated linear Dirac equation and define the relative Morse index to measure the difference between the nonlinearity at the origin and at infinity. By building
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Classification and non-degeneracy of positive radial solutions for a weighted fourth-order equation and its application Nonlinear Anal. (IF 1.4) Pub Date : 2023-12-19 Shengbing Deng, Xingliang Tian
This paper is devoted to radial solutions of the following weighted fourth-order equation div(|x|α∇(div(|x|α∇u)))=|u|2α∗∗−2uinRN,where N≥2, 4−N2<α<2 and 2α∗∗=2NN−4+2α. It is obvious that the solutions of above equation are invariant under the scaling λN−4+2α2u(λx) while they are not invariant under translation when α≠0. We characterize all the solutions to the related linearized problem about radial
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Large deviations and the emergence of a logarithmic delay in a nonlocal linearised Fisher–KPP equation Nonlinear Anal. (IF 1.4) Pub Date : 2023-12-16 Nathanaël Boutillon
We study a variant of the Fisher–KPP equation with nonlocal dispersal. Using the theory of large deviations, we show the emergence of a “Bramson-like” logarithmic delay for the linearised equation with step-like initial data. We conclude that the logarithmic delay emerges also for the solutions of the nonlinear equation. Previous papers found very precise results for the nonlinear equation with strong
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Refinement of asymptotic behavior of the eigenvalues for the linearized Liouville–Gel’fand problem Nonlinear Anal. (IF 1.4) Pub Date : 2023-12-16 Hiroshi Ohtsuka, Tomohiko Sato
We determine the second term of the asymptotic expansions for the first m eigenvalues and eigenfunctions of the linearized Liouville–Gel’fand problem associated with solutions that blow-up at m points. Our problem is the case with an inhomogeneous coefficient in a two-dimensional domain and we extend the previous studies for the problem with a homogeneous coefficient. We also discuss in detail the
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Sharp weighted Strichartz estimates and critical inhomogeneous Hartree equations Nonlinear Anal. (IF 1.4) Pub Date : 2023-12-15 Seongyeon Kim, Yoonjung Lee, Ihyeok Seo
We study the Cauchy problem for the inhomogeneous Hartree equation in this paper. Although its well-posedness theory has been extensively studied in recent years, much less is known compared to the classical Hartree model of homogeneous type. In particular, the problem of Sobolev initial data with the Sobolev critical index remains unsolved. The main contribution of this paper is to establish the local
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On a Cahn–Hilliard system with source term and thermal memory Nonlinear Anal. (IF 1.4) Pub Date : 2023-12-14 Pierluigi Colli, Gianni Gilardi, Andrea Signori, Jürgen Sprekels
A nonisothermal phase field system of Cahn–Hilliard type is introduced and analyzed mathematically. The system constitutes an extension of the classical Caginalp model for nonisothermal phase transitions with a conserved order parameter. It couples a Cahn–Hilliard type equation with source term for the order parameter with the universal balance law of internal energy. In place of the standard Fourier
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Global solutions of quasi-linear Hamiltonian mKdV equation Nonlinear Anal. (IF 1.4) Pub Date : 2023-12-08 Fangchi Yan, Qingtian Zhang
We study the initial value problem of quasi-linear Hamiltonian mKdV equations. Our goal is to prove the global-in-time existence of a solution given sufficiently smooth, localized, and small initial data. To achieve this, we utilize the bootstrap argument, Sobolev energy estimates, and the dispersive estimate. This proof relies on the space–time resonance method, as well as a bilinear estimate developed
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Remark on coisotropic Ekeland–Hofer–Zehnder capacity Nonlinear Anal. (IF 1.4) Pub Date : 2023-12-06 Kun Shi
In this paper, we give a counter-example to show that coisotropic Ekeland–Hofer–Zehnder capacities do not satisfy superadditivity for hyperplane cuts in higher dimension. Next, we show that the coisotropic Ekeland–Hofer–Zehnder capacity relative to Rn,k is not asymptotic equivalent to any normalized symplectic capacity in general case. But we show on the class of centrally symmetric convex domain in
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Stability and moduli space of generalized Ricci solitons Nonlinear Anal. (IF 1.4) Pub Date : 2023-12-06 Kuan-Hui Lee
The generalized Einstein–Hilbert action is an extension of the classic scalar curvature energy and Perelman’s F-functional which incorporates a closed three-form. The critical points are known as generalized Ricci solitons, which arise naturally in mathematical physics, complex geometry, and generalized geometry. Through a delicate analysis of the group of generalized gauge transformations, and implementing