Convergence Rate for Galerkin Approximation of the Stochastic Allen—Cahn Equations on 2D Torus

摘要: In this paper we discuss the convergence rate for Galerkin approximation of stochastic Allen-Cahn equations driven by space-time white noise on $\T$. First prove that 2D heat equation is order $\alpha-\delta$ in Besov space $\C^{-\alpha}$ $\alpha\in(0,1)$ and $\delta>0$ arbitrarily small. Then obtain $\alpha\in(0,2/9)$