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تسجيل مستخدم جديدOn the approximation for singularly perturbed stochastic wave equations
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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 asymptotic 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 $alpha>1$,.
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