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Random attractors for stochastic reaction‐diffusion equations with multiplicative noise in H 0 1
Author(s) -
Wang Gang,
Tang Yanbin
Publication year - 2014
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.201300114
Subject(s) - multiplicative noise , attractor , mathematics , random dynamical system , multiplicative function , reaction–diffusion system , order (exchange) , dynamical systems theory , diffusion , nonlinear system , mathematical analysis , noise (video) , statistical physics , stochastic simulation , linear dynamical system , statistics , physics , linear system , computer science , finance , signal transfer function , digital signal processing , quantum mechanics , artificial intelligence , analog signal , computer hardware , economics , image (mathematics) , thermodynamics
In this paper, we study the random dynamical system generated by a stochastic reaction‐diffusion equation with multiplicative noise and prove the existence of anL 2 ( D ) , H 0 1 ( D ) ‐random attractor for such a random dynamical system. The nonlinearity f is supposed to satisfy some growth of arbitrary order p − 1( p ≥ 2 ) .