Random exponential attractor for a stochastic reaction-diffusion equation in $L^{2p}(D)$

IF 3.1 3区数学 Q1 MATHEMATICS

Advances in Difference Equations Pub Date : 2024-01-02 DOI:10.1186/s13662-023-03795-z

Gang Wang, Chaozhu Hu

引用次数: 0

Abstract

In this paper, we establish some sufficient conditions for the existence of a random exponential attractor for a random dynamical system in a Banach space. As an application, we consider a stochastic reaction-diffusion equation with multiplicative noise. We show that the random dynamical system $\phi(t,\omega)$ generated by this stochastic reaction-diffusion equation is uniformly Fréchet differentiable on a positively invariant random set in $L^{2p}(D)$ and satisfies the conditions of the abstract result, then we obtain the existence of a random exponential attractor in $L^{2p}(D)$, where p is the growth of the nonlinearity satisfying $1< p\leq 3$.

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L^{2p}(D)$中随机反应扩散方程的随机指数吸引子

在本文中，我们为巴拿赫空间中随机动力系统的随机指数吸引子的存在建立了一些充分条件。作为应用，我们考虑了一个具有乘法噪声的随机反应-扩散方程。我们证明了由这个随机反应-扩散方程产生的随机动力系统 $\phi(t,\omega)$在 $L^{2p}(D)$ 中的正不变随机集上是均匀弗雷谢特可微分的，并且满足抽象结果的条件，然后我们得到在 $L^{2p}(D)$ 中存在一个随机指数吸引子，其中 p 是满足 $1<；pleq 3$.

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Advances in Difference Equations MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

8.60

自引率

0.00%

发文量

审稿时长

4-8 weeks

期刊介绍： The theory of difference equations, the methods used, and their wide applications have advanced beyond their adolescent stage to occupy a central position in applicable analysis. In fact, in the last 15 years, the proliferation of the subject has been witnessed by hundreds of research articles, several monographs, many international conferences, and numerous special sessions. The theory of differential and difference equations forms two extreme representations of real world problems. For example, a simple population model when represented as a differential equation shows the good behavior of solutions whereas the corresponding discrete analogue shows the chaotic behavior. The actual behavior of the population is somewhere in between. The aim of Advances in Difference Equations is to report mainly the new developments in the field of difference equations, and their applications in all fields. We will also consider research articles emphasizing the qualitative behavior of solutions of ordinary, partial, delay, fractional, abstract, stochastic, fuzzy, and set-valued differential equations. Advances in Difference Equations will accept high-quality articles containing original research results and survey articles of exceptional merit.