On the approximation for singularly perturbed stochastic wave equations
arXiv:1109.3000
Abstract
We explore the relation between fast waves, damping and imposed noise for different scalings by considering the singularly perturbed stochastic nonlinear wave equations νu_{tt}+u_t=\D u+f(u)+ν^α\dot{W} on a bounded spatial domain. An asymptotic approximation to the stochastic wave equation is constructed by a special transformation and splitting of $νu_{t}$. This splitting gives a clear description of the structure of $u$. The approximating model, for small $ν>0$\,, is a stochastic nonlinear heat equation for exponent $0\leqα<1$\,, and is a deterministic nonlinear wave equation for exponent $α>1$\,.
11 pages