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arXiv · 1109.3000

On the approximation for singularly perturbed stochastic wave equations

Wei Wang·Yan Lv·A. J. Roberts
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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 $α>1$\,.

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Wei Wang, Yan Lv, A. J. Roberts. 2011-09-14. On the approximation for singularly perturbed stochastic wave equations. https://arxiv.org/abs/1109.3000

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