Attractors for Stochastic Reaction-Diffusion Equation with Additive Homogeneous Noise

被引：3

作者：

Slavik, Jakub ^{[1
]}

机构：

[1] Czech Acad Sci, Inst Informat Theory & Automat, Vodarenskou Vezi 4, Prague 18200 8, Czech Republic

来源：

CZECHOSLOVAK MATHEMATICAL JOURNAL | 2021年 / 71卷 / 01期

关键词：

reaction-diffusion equation; random attractor; spatially homogeneous noise; EVOLUTION-EQUATIONS; PULLBACK ATTRACTORS; DRIVEN; EXISTENCE;

D O I：

10.21136/CMJ.2020.0144-19

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study the asymptotic behaviour of solutions of a reaction-diffusion equation in the whole space Double-struck capital R(d)driven by a spatially homogeneous Wiener process with finite spectral measure. The existence of a random attractor is established for initial data in suitable weightedL(2)-space in any dimension, which complements the result from P. W. Bates, K. Lu, and B. Wang (2013). Asymptotic compactness is obtained using elements of the method of short trajectories.

引用

页码：21 / 43

页数：23

共 50 条

[1] Attractors for Stochastic Reaction-Diffusion Equation with Additive Homogeneous Noise
Jakub Slavík
Czechoslovak Mathematical Journal, 2021, 71 : 21 - 43
[2] Dynamics for a stochastic reaction-diffusion equation with additive noise
Cao, Daomin
Sun, Chunyou
Yang, Meihua
JOURNAL OF DIFFERENTIAL EQUATIONS, 2015, 259 (03) : 838 - 872
[3] H1-random attractors for stochastic reaction-diffusion equations with additive noise
Zhao, Wenqiang
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2013, 84 : 61 - 72
[4] Attractors for the stochastic reaction-diffusion equation driven by linear multiplicative noise with a variable coefficient
Fan, Xiaoming
Chen, Huatao
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2013, 398 (02) : 715 - 728
[5] A STOCHASTIC REACTION-DIFFUSION EQUATION WITH MULTIPLICATIVE NOISE
FLANDOLI, F
APPLIED MATHEMATICS LETTERS, 1991, 4 (04) : 45 - 48
[6] Stability and random attractors for a reaction-diffusion equation with multiplicative noise
Caraballo, T
Langa, JA
Robinson, JC
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 2000, 6 (04) : 875 - 892
[7] Topological dimensions of random attractors for a stochastic reaction-diffusion equation with delay
Hu, Wenjie
Caraballo, Tomas
ELECTRONIC JOURNAL OF QUALITATIVE THEORY OF DIFFERENTIAL EQUATIONS, 2024, (56) : 1 - 23
[8] Random Dynamics of Stochastic Reaction-Diffusion Systems with Additive Noise
You, Yuncheng
JOURNAL OF DYNAMICS AND DIFFERENTIAL EQUATIONS, 2017, 29 (01) : 83 - 112
[9] Random attractors for a class of stochastic reaction-diffusion equations on RN with multiplicative noise
Li, Bowen
Jiang, Yong
Li, Xiaojun
COMPUTATIONAL AND MATHEMATICAL METHODS, 2019, 1 (04)
[10] Global Attractors of a Nonautonomous Reaction-Diffusion Equation
A. V. Kapustyan
Differential Equations, 2002, 38 : 1467 - 1471

← 1 2 3 4 5 →