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Long-time behavior of stochastic reaction-diffusion equation with dynamical boundary condition

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    * Corresponding author
The first author was supported by the NSFC grants(11361053,11471148), the Fundamental Research Funds for the Central Universities Grant (lzujbky-2016-98) and the State Scholarship Fund (201506185006) of China Scholarship Council. The second author was supported by the NSFC grant(11571125) and the NCET-12-0204.
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  • In this paper, we study the dynamic behavior of a stochastic reaction-diffusion equation with dynamical boundary condition, where the nonlinear terms $f$ and $h$ satisfy the polynomial growth condition of arbitrary order. Some higher-order integrability of the difference of the solutions near the initial time, and the continuous dependence result with respect to initial data in $H^1(\mathcal{O})× H^{\frac 1 2}(Γ)$ were established. As a direct application, we can obtain the existence of pullback random attractor $A$ in the spaces $L^{p}(\mathcal{O})× L^{p}(Γ)$ and $H^1(\mathcal{O})× H^{\frac 1 2}(Γ)$ immediately.

    Mathematics Subject Classification: Primary:37L05, 35B40;Secondary:35B41.

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