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Birkhoff Program for Geodesic Flows of Surfaces and Applications: Homoclinics J. Dyn. Diff. Equat. (IF 1.3) Pub Date : 2024-03-09 Gonzalo Contreras, Fernando Oliveira
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Chain Recurrence and Selgrade’s Theorem for Affine Flows J. Dyn. Diff. Equat. (IF 1.3) Pub Date : 2024-03-04 Fritz Colonius, Alexandre J. Santana
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Spectral Analysis and Stability of the Moore-Gibson-Thompson-Fourier Model J. Dyn. Diff. Equat. (IF 1.3) Pub Date : 2024-03-01 Monica Conti, Filippo Dell’Oro, Lorenzo Liverani, Vittorino Pata
Abstract We consider the linear evolution system $$\begin{aligned} {\left\{ \begin{array}{ll} u_{ttt}+\alpha u_{tt} + \beta \Delta ^2 u_t + \gamma \Delta ^2 u =- \eta \Delta \theta \\ \theta _t - \kappa \Delta \theta = \eta \Delta u_{tt} + \alpha \eta \Delta u_t \end{array}\right. } \end{aligned}$$ describing the dynamics of a thermoviscoelastic plate of MGT type with Fourier heat conduction. The focus
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Invariant Manifolds for a PDE-ODE Coupled System J. Dyn. Diff. Equat. (IF 1.3) Pub Date : 2024-02-28 Xingjie Yan, Kun Yin, Xin-Guang Yang, Alain Miranville
The aim of this paper is to construct invariant manifolds for a coupled system, consisting of a parabolic equation and a second-order ordinary differential equation, set on \(\mathbb {T}^3\) and subject to periodic boundary conditions. Notably, the “spectral gap condition" does not hold for the system under consideration, leading to the use of the spatial averaging principle, together with the graph
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Rigidity and Absolute Continuity of Foliations of Anosov Endomorphisms J. Dyn. Diff. Equat. (IF 1.3) Pub Date : 2024-02-26 Fernando Micena
We found a dichotomy involving rigidity and measure of maximal entropy of a \(C^{\infty }\)-special Anosov endomorphism of the 2-torus. Considering \(\widetilde{m} \) the measure of maximal entropy of a \(C^{\infty }\)-special Anosov endomorphism of the 2-torus, either \(\widetilde{m}\) satisfies the Pesin formula (in this case we get smooth conjugacy with the linearization) or there is a set Z, such
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Dynamical Systems on Graph Limits and Their Symmetries J. Dyn. Diff. Equat. (IF 1.3) Pub Date : 2024-02-23
Abstract The collective dynamics of interacting dynamical units on a network crucially depends on the properties of the network structure. Rather than considering large but finite graphs to capture the network, one often resorts to graph limits and the dynamics thereon. We elucidate the symmetry properties of dynamical systems on graph limits—including graphons and graphops—and analyze how the symmetry
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Long Term Behavior of 2D and 3D Non-autonomous Random Convective Brinkman–Forchheimer Equations Driven by Colored Noise J. Dyn. Diff. Equat. (IF 1.3) Pub Date : 2024-02-23 Kush Kinra, Manil T. Mohan
The long time behavior of Wong–Zakai approximations of 2D as well as 3D non-autonomous stochastic convective Brinkman–Forchheimer (CBF) equations with non-linear diffusion terms on some bounded and unbounded domains is discussed in this work. To establish the existence of pullback random attractors, the concept of asymptotic compactness (AC) is used. In bounded domains, AC is proved via compact Sobolev
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Synchronization and Random Attractors in Reaction Jump Processes J. Dyn. Diff. Equat. (IF 1.3) Pub Date : 2024-02-23 Maximilian Engel, Guillermo Olicón-Méndez, Nathalie Wehlitz, Stefanie Winkelmann
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Stability Analysis of Random Attractors for Stochastic Modified Swift–Hohenberg Equations with Delays J. Dyn. Diff. Equat. (IF 1.3) Pub Date : 2024-02-23 Qiangheng Zhang, Tomás Caraballo, Shuang Yang
A new type of random attractors is introduced to study dynamics of a stochastic modified Swift–Hohenberg equation with a general delay. A compact, pullback attracting and dividedly invariant set is called a backward attractor, while the criteria for its existence are established in terms of increasing dissipation and backward asymptotic compactness of a cocycle. If the delay term in the equation is
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Density of the Level Sets of the Metric Mean Dimension for Homeomorphisms J. Dyn. Diff. Equat. (IF 1.3) Pub Date : 2024-02-10
Abstract Let N be an n-dimensional compact riemannian manifold, with \(n\ge 2\) . In this paper, we prove that for any \(\alpha \in [0,n]\) , the set consisting of homeomorphisms on N with lower and upper metric mean dimensions equal to \(\alpha \) is dense in \(\text {Hom}(N)\) . More generally, given \(\alpha ,\beta \in [0,n]\) , with \(\alpha \le \beta \) , we show the set consisting of homeomorphisms
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Global Well-Posedness to the n-Dimensional Compressible Oldroyd-B Model Without Damping Mechanism J. Dyn. Diff. Equat. (IF 1.3) Pub Date : 2024-02-05 Xiaoping Zhai, Zhi-Min Chen
We are concerned with the global well-posedness to the compressible Oldroyd-B model without a damping term in the stress tensor equation. By exploiting the intrinsic structure of the equations and introducing several new quantities for the density, the velocity and the divergence of the stress tensor, we overcome the difficulty of the lack of dissipation for the density and the stress tensor, and construct
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Stability and Instability of Equilibria in Age-Structured Diffusive Populations J. Dyn. Diff. Equat. (IF 1.3) Pub Date : 2024-02-05 Christoph Walker
The principle of linearized stability and instability is established for a classical model describing the spatial movement of an age-structured population with nonlinear vital rates. It is shown that the real parts of the eigenvalues of the corresponding linearization at an equilibrium determine the latter’s stability or instability. The key ingredient of the proof is the eventual compactness of the
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Multiscale Conditional Shadowing J. Dyn. Diff. Equat. (IF 1.3) Pub Date : 2024-02-01
Abstract In this paper, we study conditional shadowing for a nonautonomous system in a Banach space assuming that the linear part admits a family of invariant subspaces (scale) with different behavior of trajectories. Conditions of shadowing are formulated in terms of smallness of the projections of one-step errors to the scale and of smallness of Lipschitz constants of the projections of nonlinear
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Shadowing for Local Homeomorphisms, with Applications to Edge Shift Spaces of Infinite Graphs J. Dyn. Diff. Equat. (IF 1.3) Pub Date : 2024-01-28 Daniel Gonçalves, Bruno B. Uggioni
In this paper, we develop the basic theory of the shadowing property for local homeomorphisms of metric locally compact spaces, with a focus on applications to edge shift spaces connected with C*-algebra theory. For the local homeomorphism (the Deaconu–Renault system) associated with a directed graph, we completely characterize the shadowing property in terms of conditions on sets of paths. Using these
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Continuity of the Unbounded Attractors for a Fractional Perturbation of a Scalar Reaction-Diffusion Equation J. Dyn. Diff. Equat. (IF 1.3) Pub Date : 2024-01-23 Maykel Belluzi, Matheus C. Bortolan, Ubirajara Castro, Juliana Fernandes
In this work we study the continuity (both upper and lower semicontinuity), defined using the Hausdorff semidistance, of the unbounded attractors for a family of fractional perturbations of a scalar reaction-diffusion equation with a non-dissipative nonlinear term.
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Comment on: Criteria for Strong and Weak Random Attractors J. Dyn. Diff. Equat. (IF 1.3) Pub Date : 2024-01-23 Hans Crauel, Sarah Geiss, Michael Scheutzow
In the article ’Criteria for Strong and Weak Random Attractors’ necessary and sufficient conditions for strong attractors and weak attractors are studied. In this note we correct two of its theorems on strong attractors.
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Hyperbolicity and Rigidity for Fibred Partially Hyperbolic Systems J. Dyn. Diff. Equat. (IF 1.3) Pub Date : 2024-01-23 Sankhadip Chakraborty, Marcelo Viana
Every volume-preserving accessible centre-bunched fibred partially hyperbolic system with 2-dimensional centre either (a) has two distinct centre Lyapunov exponents, or (b) exhibits an invariant continuous line field (or pair of line fields) tangent to the centre leaves, or (c) admits a continuous conformal structure on the centre leaves invariant under both the dynamics and the stable and unstable
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Delta Shocks as Solutions of Conservation Laws with Discontinuous Moving Source J. Dyn. Diff. Equat. (IF 1.3) Pub Date : 2024-01-22 C. O. R. Sarrico
A Riemann problem for the conservation law \(u_{t}+[\phi (u)]_{x}=kH(x-vt)\), where x, t, k, v and \(u=u(x,t)\) are real numbers, is studied with the goal of getting singular solutions in a convenient space of distributions that contains delta shock waves. Here \(\phi \) stands for an entire function taking real values on the real axis and H represents the Heaviside function. When u is seen as a density
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Rayleigh–Bénard Convection with Stochastic Forcing Localised Near the Bottom J. Dyn. Diff. Equat. (IF 1.3) Pub Date : 2024-01-19 Juraj Földes, Armen Shirikyan
We prove stochastic stability of the three-dimensional Rayleigh–Bénard convection in the infinite Prandtl number regime for any pair of temperatures maintained on the top and the bottom. Assuming that the non-degenerate random perturbation acts in a thin layer adjacent to the bottom of the domain, we prove that the law of the random flow periodic in the two infinite directions stabilises to a unique
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The Existence of Isolating Blocks for Multivalued Semiflows J. Dyn. Diff. Equat. (IF 1.3) Pub Date : 2024-01-19 Estefani M. Moreira, José Valero
In this article, we show the existence of an isolating block, a special neighborhood of an isolated invariant set, for multivalued semiflows acting on metric spaces (not locally compact). Isolating blocks play an important role in Conley’s index theory for single-valued semiflows and are used to define the concepts of homology index. Although Conley’s index was generalized in the context of multivalued
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Existence of Global Entropy Solution for Eulerian Droplet Models and Two-phase Flow Model with Non-constant Air Velocity J. Dyn. Diff. Equat. (IF 1.3) Pub Date : 2024-01-13 Abhrojyoti Sen, Anupam Sen
This article addresses the question concerning the existence of global entropy solution for generalized Eulerian droplet models with air velocity depending on both space and time variables. When \(f(u)=u,\) \(\kappa (t)=const.\) and \(u_a(x,t)=const.\) in (1.1), the study of the Riemann problem has been carried out by Keita and Bourgault (J Math Anal Appl 472(1):1001–1027, 2019) and Zhang et al. (Appl
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Dichotomies for Triangular Systems via Admissibility J. Dyn. Diff. Equat. (IF 1.3) Pub Date : 2024-01-13 Davor Dragičević, Kenneth J. Palmer
In this article we study the relationship between the exponential dichotomy properties of a triangular system of linear difference equations and its associated diagonal system. We use admissibility to give new shorter proofs of results obtained in Battelli et al. (J Differ Equ Appl 28:1054–1086, 2022) and we also establish new necessary and sufficient conditions that the diagonal system have a dichotomy
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Higher-Order Continuity of Pullback Random Attractors for Random Quasilinear Equations with Nonlinear Colored Noise J. Dyn. Diff. Equat. (IF 1.3) Pub Date : 2024-01-10 Yangrong Li, Fengling Wang, Tomás Caraballo
For a nonautonomous random dynamical system, we introduce a concept of a pullback random bi-spatial attractor (PRBA). We prove an existence theorem of a PRBA, which includes its measurability, compactness and attraction in the regular space. We then establish the residual dense continuity of a family of PRBAs from a parameter space into the space of all compact subsets of the regular space equipped
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The Stability Region for Schur Stable Trinomials with General Complex Coefficients J. Dyn. Diff. Equat. (IF 1.3) Pub Date : 2023-12-16 Gerardo Barrera, Waldemar Barrera, Juan Pablo Navarrete
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Hypocoercivity in Algebraically Constrained Partial Differential Equations with Application to Oseen Equations J. Dyn. Diff. Equat. (IF 1.3) Pub Date : 2023-12-08 Franz Achleitner, Anton Arnold, Volker Mehrmann
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The Szymczak Functor and Shift Equivalence on the Category of Finite Sets and Finite Relations J. Dyn. Diff. Equat. (IF 1.3) Pub Date : 2023-12-09 Mateusz Przybylski, Marian Mrozek, Jim Wiseman
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On the Failure of Linearization for Germs of $$C^1$$ Hyperbolic Vector Fields in Dimension One J. Dyn. Diff. Equat. (IF 1.3) Pub Date : 2023-12-05 Hélène Eynard-Bontemps, Andrés Navas
We investigate conjugacy classes of germs of hyperbolic 1-dimensional vector fields at the origin in low regularity. We show that the classical linearization theorem of Sternberg strongly fails in this setting by providing explicit uncountable families of mutually non-conjugate flows with the same multipliers, where conjugacy is considered in the bi-Lipschitz, \(C^1\) and \(C^{1+ac}\) settings.
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Center Stable Manifolds Around Line Solitary Waves of the Zakharov–Kuznetsov Equation J. Dyn. Diff. Equat. (IF 1.3) Pub Date : 2023-11-27 Yohei Yamazaki
In this paper, we construct center stable manifolds of unstable line solitary waves for the Zakharov–Kuznetsov equation on \({\mathbb {R}} \times {\mathbb {T}}_L\) and show the orbital stability of the unstable line solitary waves on the center stable manifolds, which yields the asymptotic stability of unstable solitary waves on the center stable manifolds near by stable line solitary waves. The construction
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Well-Posedness and Singularity Formation for the Kolmogorov Two-Equation Model of Turbulence in 1-D J. Dyn. Diff. Equat. (IF 1.3) Pub Date : 2023-11-06 Francesco Fanelli, Rafael Granero-Belinchón
We study the Kolomogorov two-equation model of turbulence in one space dimension. Two are the main results of the paper. First of all, we establish a local well-posedness theory in Sobolev spaces even in the case of vanishing mean turbulent kinetic energy. Then, we show that there are smooth solutions which blow up in finite time. To the best of our knowledge, these results are the first establishing
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Dynamics of Interacting Monomial Scalar Field Potentials and Perfect Fluids J. Dyn. Diff. Equat. (IF 1.3) Pub Date : 2023-11-06 Artur Alho, Vitor Bessa, Filipe C. Mena
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Boundedness and Stabilization in a Stage-Structured Predator–Prey Model with Two Taxis Mechanisms J. Dyn. Diff. Equat. (IF 1.3) Pub Date : 2023-10-27 Changfeng Liu, Shangjiang Guo
In this paper, we investigate a predator–prey system with stage structure for the predator under Neumann boundary condition, which has not only the taxis mechanism caused by the interaction between mature predator and prey, but also contains the taxis mechanism generated by the interaction between mature predator and immature predator. Regardless of the strength of the chemotactic coefficient, the
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On weak/Strong Attractor for a 3-D Structural-Acoustic Interaction with Kirchhoff–Boussinesq Elastic Wall Subject to Restricted Boundary Dissipation J. Dyn. Diff. Equat. (IF 1.3) Pub Date : 2023-10-28 Irena Lasiecka, José H. Rodrigues
Existence of global attractors for a structural-acoustic system, subject to restricted boundary dissipation, is considered. Dynamics of the acoustic environment is given by a linear 3-D wave equation subject to locally distributed boundary dissipation, while the dynamics on the (flat) structural wall is given by a 2D-Kirchhoff-Boussinesq plate equation, subject to linear dissipation and supercritical
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On the Topological Entropy of Saturated Sets for Amenable Group Actions J. Dyn. Diff. Equat. (IF 1.3) Pub Date : 2023-10-27 Xiankun Ren, Xueting Tian, Yunhua Zhou
Let (X, G) be a G-action topological system, where G is a countable infinite discrete amenable group and X a compact metric space. We prove a variational principle for topological entropy of saturated sets for systems which have the specification property and uniform separation property. We show that certain algebraic actions satisfy these two conditions. We give an application in multifractal analysis
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An Optimal Halanay Inequality and Decay Rate of Solutions to Some Classes of Nonlocal Functional Differential Equations J. Dyn. Diff. Equat. (IF 1.3) Pub Date : 2023-10-21 Tran Dinh Ke, Nguyen Nhu Thang
In this work, we prove a nonlocal Halanay inequality with an exact decay rate. This enables us to analyze behavior of solutions to some classes of nonlocal ODEs and PDEs involving unbounded delays. The obtained results extend and improve the previous ones proved for fractional differential equations and other nonlocal subdiffusion equations.
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Quantifying the Shadowing Property J. Dyn. Diff. Equat. (IF 1.3) Pub Date : 2023-10-20 C. A. Morales, T. Nguyen
In this paper, we present a revised formulation of the Lipschitz shadowing property introduced by Pilyugin and Tikhomirov (Nonlinearity 23:2509–2515, 2010), which involves a numerical quantity known as the “Lipschitz shadowability constant.” This constant is computed for an invertible operator within a Banach space, by taking the reciprocal of the operator’s shadowability constant. We provide a detailed
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Vanishing-Spreading Dichotomy in a Two-Species Chemotaxis Competition System with a Free Boundary J. Dyn. Diff. Equat. (IF 1.3) Pub Date : 2023-10-20 Lianzhang Bao, Wenxian Shen
Predicting the evolution of expanding population is critical to control biological threats such as invasive species and virus explosion. In this paper, we consider a two species chemotaxis system of parabolic-parabolic-elliptic type with Lotka–Volterra type competition terms and a free boundary. Such a model with a free boundary describes the spreading of new or invasive species subject to the influence
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The 3-D Nonlinear Hyperbolic–Parabolic Problems: Invariant Manifolds J. Dyn. Diff. Equat. (IF 1.3) Pub Date : 2023-10-20 Rong-Nian Wang, Jia-Cheng Zhao
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Dichotomy Gap Conditions, Admissible Spaces, and Inertial Manifolds J. Dyn. Diff. Equat. (IF 1.3) Pub Date : 2023-10-20 Thieu Huy Nguyen, Thi Ngoc Ha Vu
We study the existence of an inertial manifold for the fully non-autonomous evolution equation of the form $$\begin{aligned} \frac{du}{dt} + A(t)u(t) = f(t,u),\, t\in \mathbb {R}, \end{aligned}$$ in certain admissible spaces. We prove the existence of such an inertial manifold in the cases that the family of linear partial differential operators \((A(t))_{t\in \mathbb {R}}\) generates an evolution
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A Note on the Polynomially Attracting Sets for Dynamical Systems J. Dyn. Diff. Equat. (IF 1.3) Pub Date : 2023-10-20 Xiangming Zhu, Chengkui Zhong
It is well-known that exponential attractor is an important concept to study the exponentially attracting rate of a compact set for dynamical systems. But recently, Zhao (Appl Math Lett, 2022. https://doi.org/10.1016/j.aml.2021.107791) studied the polynomially attracting sets for a class of wave equations: $$\begin{aligned} u_{tt}-\Delta u+k\Vert u_{t}\Vert ^{p}u_{t}+f(u)=\int _{\Omega }K(x,y)u_{t}(t
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Nonautonomous Normal Forms with Parameters J. Dyn. Diff. Equat. (IF 1.3) Pub Date : 2023-10-20 Luís Barreira, Claudia Valls
For a nonautonomous dynamics with discrete time depending on a parameter, we construct normal forms that have the same regularity as the original dynamics. A principal difficulty is that the resonances may depend on the parameter. The proof consists of three main elements that are interesting in their own right. First, we show that the spectrum of a nonautonomous linear dynamics does not vary much
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Stability of Some Anticipating Semilinear Stochastic Differential Equations of Skorohod Type J. Dyn. Diff. Equat. (IF 1.3) Pub Date : 2023-10-11 Jorge A. León, David Márquez-Carreras, Josep Vives
In the present paper, we study different types of stability of the solution of a semi-linear anticipating stochastic differential equation driven by a Brownian motion, with a random variable as initial condition. The involved stochastic integral is the Skorohod one. Being the initial condition random, we need to redefine the stability concepts. The new stability criteria depend on the derivative of
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Block Regularisation of the Logarithm Central Force Problem J. Dyn. Diff. Equat. (IF 1.3) Pub Date : 2023-10-06 Archishman Saha, Cristina Stoica
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Coherent Structures in Nonlocal Systems: Functional Analytic Tools J. Dyn. Diff. Equat. (IF 1.3) Pub Date : 2023-10-05 Olivia Cannon, Arnd Scheel
We develop tools for the analysis of fronts, pulses, and wave trains in spatially extended systems with nonlocal coupling. We first determine Fredholm properties of linear operators, thereby identifying pointwise invertibility of the principal part together with invertibility at spatial infinity as necessary and sufficient conditions. We then build on the Fredholm theory to construct center manifolds
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Spectra Based on Bohl Exponents and Bohl Dichotomy for Nonautonomous Difference Equations J. Dyn. Diff. Equat. (IF 1.3) Pub Date : 2023-10-05 Adam Czornik, Konrad Kitzing, Stefan Siegmund
For nonautonomous linear difference equations with bounded coefficients on \(\mathbb {N}\) which have a bounded inverse, we introduce two different notions of spectra and discuss their relation to the well-known exponential dichotomy spectrum. The first new spectral notion is called Bohl spectrum and is based on an extended notion of the concept of Bohl exponents. The second new spectral notion is
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Smooth Anosov Katok Diffeomorphisms with Generic Measure J. Dyn. Diff. Equat. (IF 1.3) Pub Date : 2023-10-05 Divya Khurana
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Reaction–Diffusion Problems on Time-Periodic Domains J. Dyn. Diff. Equat. (IF 1.3) Pub Date : 2023-09-23 Jane Allwright
Reaction–diffusion equations are studied on bounded, time-periodic domains with zero Dirichlet boundary conditions. The long-time behaviour is shown to depend on the principal periodic eigenvalue of a transformed periodic-parabolic problem. We prove upper and lower bounds on this eigenvalue under a range of different assumptions on the domain, and apply them to examples. The principal eigenvalue is
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Generalized Pitchfork Bifurcations in D-Concave Nonautonomous Scalar Ordinary Differential Equations J. Dyn. Diff. Equat. (IF 1.3) Pub Date : 2023-09-23 Jesús Dueñas, Carmen Núñez, Rafael Obaya
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Topological Inference of the Conley Index J. Dyn. Diff. Equat. (IF 1.3) Pub Date : 2023-09-23 Ka Man Yim, Vidit Nanda
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Decomposition of Linear Systems on Disconnected Lie Groups J. Dyn. Diff. Equat. (IF 1.3) Pub Date : 2023-09-15 Josiney A. Souza
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Enhanced Dissipation for Stochastic Navier–Stokes Equations with Transport Noise J. Dyn. Diff. Equat. (IF 1.3) Pub Date : 2023-09-15 Dejun Luo
The phenomenon of dissipation enhancement by transport noise is shown for stochastic 2D Navier–Stokes equations in velocity form. In the 3D case, suppression of blow-up is proved for stochastic Navier–Stokes equations in vorticity form; in particular, quantitative estimate allows us to choose the parameters of noise, uniformly in initial vorticity bounded in \(L^2\)-norm, so that global solutions exist
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Spatiotemporal Evolution of Coinfection Dynamics: A Reaction–Diffusion Model J. Dyn. Diff. Equat. (IF 1.3) Pub Date : 2023-09-15 Thi Minh Thao Le, Sten Madec
This paper investigates the impact of spatial heterogeneity on the interaction between similar strains in a dynamical system of coinfecting strains with spatial diffusion. The SIS model studied is a reaction–diffusion system with spatially heterogeneous coefficients. The study considers two limiting cases: asymptotically slow and fast diffusion coefficients. When the diffusion coefficient is small
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Global Dynamics of a Diffusive Lotka–Volterra Competition Model with Stage-Structure J. Dyn. Diff. Equat. (IF 1.3) Pub Date : 2023-09-15 Li Ma, Shangjiang Guo
In this paper, we investigate the global dynamics of a Lotka–Volterra competition–diffusion system with stage structure, general intrinsic growth rates and carrying capacities for two competing species in heterogeneous environments, in which each of two competing populations chooses its diffusion strategy as the tendency to have a distribution proportional to a certain positive prescribed function
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Delay-Difference Equations and Stability J. Dyn. Diff. Equat. (IF 1.3) Pub Date : 2023-09-02 Luís Barreira, Claudia Valls
For any linear delay-difference equation with constant coefficients, we show that the existence of an exponential dichotomy is equivalent to the Ulam–Hyers stability of the equation. This generalizes former work for scalar equations, with a substantial simplification of former arguments. We also show that the same equivalence holds for any linear delay-difference equation (with scalar coefficients
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Zabczyk Type Criteria for Asymptotic Behavior of Dynamical Systems and Applications J. Dyn. Diff. Equat. (IF 1.3) Pub Date : 2023-08-29 Davor Dragičević, Adina Luminiţa Sasu, Bogdan Sasu, Ana Şirianţu
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Dynamics of a Predator–Prey Model with Memory-Based Diffusion J. Dyn. Diff. Equat. (IF 1.3) Pub Date : 2023-08-27 Yujia Wang, Chuncheng Wang, Dejun Fan, Yuming Chen
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Propagation Dynamics for Time–Space Periodic and Partially Degenerate Reaction–Diffusion Systems with Time Delay J. Dyn. Diff. Equat. (IF 1.3) Pub Date : 2023-08-27 Mingdi Huang, Shi-Liang Wu, Xiao-Qiang Zhao
This paper is concerned with the propagation dynamics of a large class of time–space periodic and partially degenerate reaction–diffusion systems with time delay and monostable nonlinearity. In the cooperative case, based on the theory of principal eigenvalues for linear and partially degenerate systems with time delay, we establish the existence of spreading speeds and its coincidence with the minimal
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Scattering and Minimization Theory for Cubic Inhomogeneous Nls with Inverse Square Potential J. Dyn. Diff. Equat. (IF 1.3) Pub Date : 2023-08-27 Hichem Hajaiej, Tingjian Luo, Ying Wang
In this paper, we study the scattering theory for the cubic inhomogeneous Schrödinger equations with inverse square potential \(iu_t+\Delta u-\frac{a}{|x|^2}u=\lambda |x|^{-b}|u|^2u\) with \(a>-\frac{1}{4}\) and \(0
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Periodic Solutions for a Class of Semilinear Euler–Bernoulli Beam Equations with Variable Coefficients J. Dyn. Diff. Equat. (IF 1.3) Pub Date : 2023-08-14 Hui Wei, Shuguan Ji
This paper is devoted to the study of periodic solutions for a class of semilinear Euler–Bernoulli beam equations with variable coefficients. Such a mathematical model is used to describe the infinitesimal, free, undamped in-plane bending vibrations of a thin straight elastic beam. When the frequency is rational, we acquire some fundamental properties of the variable coefficients beam operator and
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Stability of Solutions to Functional KPP-Fisher Equations J. Dyn. Diff. Equat. (IF 1.3) Pub Date : 2023-08-14 Abraham Solar
We study the stability properties of semi-wavefronts of the KPP-Fisher equation with infinite delay \(\frac{\partial }{\partial t}u(t, x)=\frac{\partial ^2 }{\partial x^2}u(t, x)+\int _{0}^{+\infty }u(t-s, x)d\mu _1(s)\Big (1-\int _0^{+\infty }u(t-s, x)d\mu _2(s)\Big ), \, t>0, \, x\in {\mathbb R},\) where \(\mu _1\) and \(\mu _2\) are Borel measures. We show an interesting property about the non convergence
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Quasi-periodic Solutions for Completely Resonant Quintic Beam Equations J. Dyn. Diff. Equat. (IF 1.3) Pub Date : 2023-08-07 Qi Li, Yixian Gao, Yong Li