Stability of stochastic reaction-diffusion equation under random influences in high regular spaces

In this paper, we systematically study the high-order stability of stochastic reaction-diffusion equation driven by additive noise as intensity vanishes. First, with a general assumption on nonlinear term, obtain convergence solutions and upper semi-continuity random attractors in L2(RN). Second, using decomposition method, technically establish Lp(RN)∩H1(RN)(p>2), therefore, is proved, where p growth exponent nonlinearity. Finally, induction argument, prove that solution uniformly bounded near initial time Lδ(RN) for arbitrary δ > p, which space are also established.