scholarly journals Multi-valued random dynamics of stochastic wave equations with infinite delays

2022 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Jingyu Wang ◽  
Yejuan Wang ◽  
Tomás Caraballo
Keyword(s):  
Asymptotic Behavior ◽  
Wave Equations ◽  
Growth Conditions ◽  
Asymptotic Behavior Of Solutions ◽  
Pullback Attractor ◽  
Lipschitz Continuous ◽  
Infinite Delays ◽  
Stochastic Wave Equations ◽  
Additive White Noise ◽  
Stochastic Wave Equation

<p style='text-indent:20px;'>This paper is devoted to the asymptotic behavior of solutions to a non-autonomous stochastic wave equation with infinite delays and additive white noise. The nonlinear terms of the equation are not expected to be Lipschitz continuous, but only satisfy continuity assumptions along with growth conditions, under which the uniqueness of the solutions may not hold. Using the theory of multi-valued non-autonomous random dynamical systems, we prove the existence and measurability of a compact global pullback attractor.</p>

Attractors for multi-valued lattice dynamical systems with nonlinear diffusion terms

2021 ◽  
Author(s):  
Panpan Zhang ◽  
Anhui Gu
Keyword(s):  
Dynamical Systems ◽  
Nonlinear Diffusion ◽  
Upper Semicontinuity ◽  
Growth Conditions ◽  
Pullback Attractor ◽  
Random Lattice ◽  
Lipschitz Continuous ◽  
Lattice Dynamical Systems ◽  
Long Term Behavior

This paper is devoted to the long-term behavior of nonautonomous random lattice dynamical systems with nonlinear diffusion terms. The nonlinear drift and diffusion terms are not expected to be Lipschitz continuous but satisfy the continuity and growth conditions. We first prove the existence of solutions, and establish the existence of a multi-valued nonautonomous cocycle. We then show the existence and uniqueness of pullback attractors parameterized by sample parameters. Finally, we establish the measurability of this pullback attractor by the method based on the weak upper semicontinuity of the solutions.

scholarly journals Asymptotic behavior of non-autonomous fractional p-Laplacian equations driven by additive noise on unbounded domains

2020 ◽  
pp. 2050020
Author(s):  
Renhai Wang ◽  
Bixiang Wang
Keyword(s):  
Asymptotic Behavior ◽  
Existence And Uniqueness ◽  
Additive Noise ◽  
Random Coefficients ◽  
Asymptotic Behavior Of Solutions ◽  
Uniqueness Of Solutions ◽  
Additive White Noise ◽  
Approach Zero ◽  
Drift Terms ◽  
Laplacian Equations

This paper deals with the asymptotic behavior of solutions to non-autonomous, fractional, stochastic [Formula: see text]-Laplacian equations driven by additive white noise and random terms defined on the unbounded domain [Formula: see text]. We first prove the existence and uniqueness of solutions for polynomial drift terms of arbitrary order. We then establish the existence and uniqueness of pullback random attractors for the system in [Formula: see text]. This attractor is further proved to be a bi-spatial [Formula: see text]-attractor for any [Formula: see text], which is compact, measurable in [Formula: see text] and attracts all random subsets of [Formula: see text] with respect to the norm of [Formula: see text]. Finally, we show the robustness of these attractors as the intensity of noise and the random coefficients approach zero. The idea of uniform tail-estimates as well as the method of higher-order estimates on difference of solutions are employed to derive the pullback asymptotic compactness of solutions in [Formula: see text] for [Formula: see text] in order to overcome the non-compactness of Sobolev embeddings on [Formula: see text] and the nonlinearity of the fractional [Formula: see text]-Laplace operator.

Global Existence and Asymptotic Behavior of Solutions for Nonlinear Wave Equations

2014 ◽  
Vol 490-491 ◽  
pp. 327-330
Author(s):  
Ji Bing Zhang ◽  
Yun Zhu Gao
Keyword(s):  
Asymptotic Behavior ◽  
Global Existence ◽  
Nonlinear Wave ◽  
Wave Equations ◽  
Nonlinear Damping ◽  
Nonlinear Wave Equations ◽  
Asymptotic Behavior Of Solutions ◽  
Potential Well ◽  
Source Terms ◽  
Damping And Source Terms

In this paper, we concern with the nonlinear wave equations with nonlinear damping and source terms. By using the potential well method, we obtain a result for the global existence and asymptotic behavior of the solutions.

scholarly journals Global Existence and Asymptotic Behavior of Solutions for a Class of Nonlinear Degenerate Wave Equations

2007 ◽  
Vol 2007 ◽  
pp. 1-9 ◽  
Author(s):  
Yaojun Ye
Keyword(s):  
Asymptotic Behavior ◽  
Wave Equations ◽  
Decay Estimate ◽  
Global Solutions ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Asymptotic Behavior Of Solutions ◽  
Potential Well ◽  
Initial Boundary Value ◽  
Nonlinear Degenerate

This paper studies the existence of global solutions to the initial-boundary value problem for some nonlinear degenerate wave equations by means of compactness method and the potential well idea. Meanwhile, we investigate the decay estimate of the energy of the global solutions to this problem by using a difference inequality.

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