Abstract
AbstractIn 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 $\phi(t,\omega)$
ϕ
(
t
,
ω
)
generated by this stochastic reaction-diffusion equation is uniformly Fréchet differentiable on a positively invariant random set in $L^{2p}(D)$
L
2
p
(
D
)
and satisfies the conditions of the abstract result, then we obtain the existence of a random exponential attractor in $L^{2p}(D)$
L
2
p
(
D
)
, where p is the growth of the nonlinearity satisfying $1< p\leq 3$
1
<
p
≤
3
.
Funder
National Natural Science Foundation of China
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,Algebra and Number Theory,Analysis