Averaging approximation to singularly perturbed nonlinear stochastic wave equations

Details Averaging approximation to singularly perturbed nonlinear stochastic wave equations Averaging approximation to singularly perturbed nonlinear stochastic wave equations

2011-07-21

arxiv.org/abs/1107.4184v1

Mathematics

Analysis of PDEs

16 pages. Submitted

Scientific paper

An averaging method is applied to derive effective approximation to the following singularly perturbed nonlinear stochastic damped wave equation \nu u_{tt}+u_t=\D u+f(u)+\nu^\alpha\dot{W} on an open bounded domain $D\subset\R^n$\,, $1\leq n\leq 3$\,. Here $\nu>0$ is a small parameter characterising the singular perturbation, and $\nu^\alpha$\,, $0\leq \alpha\leq 1/2$\,, 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)+\nu^\alpha\dot{W} to an error of $\ord{\nu^\alpha}$\,.

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