Random exponential attractor for a stochastic reaction-diffusion equation in $L^{2p}(D)$
Tóm tắt
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 $1< p\leq 3$ .
Tài liệu tham khảo
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