Approximating dynamics of a singularly perturbed stochastic wave equation with a random dynamical boundary condition

Guanggan Chen; Jinqiao Duan; Jian Zhang

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arXiv · 1208.5947

Approximating dynamics of a singularly perturbed stochastic wave equation with a random dynamical boundary condition

Guanggan Chen·Jinqiao Duan·Jian Zhang

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Abstract

This work is concerned with a singularly perturbed stochastic nonlinear wave equation with a random dynamical boundary condition. A splitting skill is used to derive the approximating equation of the system in the sense of probability distribution, when the singular perturbation parameter is sufficiently small. The approximating equation is a stochastic parabolic equation when the power exponent of singular perturbation parameter is in $[1/2, 1)$, but a deterministic hyperbolic (wave) equation when the power exponent is in $(1, +\infty)$.

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Guanggan Chen, Jinqiao Duan, Jian Zhang. 2012-08-29. Approximating dynamics of a singularly perturbed stochastic wave equation with a random dynamical boundary condition. https://arxiv.org/abs/1208.5947

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