Averaging approximation to singularly perturbed nonlinear stochastic wave equations

Abstract

An averaging method is applied to derive effective approximation to the following singularly perturbed nonlinear stochastic damped wave equation νu_{tt}+u_t=\D u+f(u)+ν^α\dot{W} on an open bounded domain $D\subset {\mathbb{R}}^n$\,, $1\le n\le 3$\,. Here $\nu >0$ is a small parameter characterising the singular perturbation, and ${\nu }^{\alpha }$\,, $0\le \alpha \le 1/2$\,, parametrises the strength of the noise. Some scaling transformations and the martingale representation theorem yield the following effective approximation for small $\nu$, u_t=\D u+f(u)+ν^α\dot{W} to an error of $\ord{ν^α}$\,.

16 pages. Submitted

References in corpus (1)

• Normal form transforms separate slow and fast modes in stochastic dynamical systems