APPROXIMATING DYNAMICS OF A SINGULARLY PERTURBED STOCHASTIC WAVE EQUATION WITH A RANDOM DYNAMICAL BOUNDARY CONDITION

This work is concerned with a singularly perturbed stochastic nonlinear wave equation with a random dynamical boundary condition. A splitting is used to establish the approximating equation of the system for a sufficiently small singular perturbation parameter. The approximating equation is a stochastic parabolic equation when the power exponent of the singular perturbation parameter is in [1/2, 1) but is a deterministic wave equation when the power exponent is in (1, +infinity). Moreover, if the power exponent of a singular perturbation parameter is bigger than or equal to 1/2, the same limiting equation of the system is derived in the sense of distribution, as the perturbation parameter tends to zero. This limiting equation is a deterministic parabolic equation.