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115 - Wei Wang , Yan Lv , A. J. Roberts 2011
We explore the relation between fast waves, damping and imposed noise for different scalings by considering the singularly perturbed stochastic nonlinear wave equations u u_{tt}+u_t=D u+f(u)+ u^alphadot{W} on a bounded spatial domain. An asymptoti c approximation to the stochastic wave equation is constructed by a special transformation and splitting of $ u u_{t}$. This splitting gives a clear description of the structure of $u$. The approximating model, for small $ u>0$,, is a stochastic nonlinear heat equation for exponent $0leqalpha<1$,, and is a deterministic nonlinear wave equation for exponent $alpha>1$,.
101 - Yan Lv , A. J. Roberts 2011
An averaging method is applied to derive effective approximation to the following singularly perturbed nonlinear stochastic damped wave equation u u_{tt}+u_t=D u+f(u)+ u^alphadot{W} on an open bounded domain $DsubsetR^n$,, $1leq nleq 3$,. Here $ u>0 $ is a small parameter characterising the singular perturbation, and $ u^alpha$,, $0leq alphaleq 1/2$,, parametrises the strength of the noise. Some scaling transformations and the martingale representation theorem yield the following effective approximation for small $ u$, u_t=D u+f(u)+ u^alphadot{W} to an error of $ord{ u^alpha}$,.
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