Approximating dynamics of a singularly perturbed stochastic wave equation with a random dynamical boundary condition (Q2870590)

The paper discusses the stochastic wave equation NEWLINE\[NEWLINE\begin{cases} \varepsilon u_{tt}^\varepsilon+u_t^\varepsilon-\Delta u^\varepsilon +u^\varepsilon-\sin(u^\varepsilon)=\varepsilon^\alpha\dot W_1\quad&\text{on}\;D \\ \varepsilon\delta_{tt}^\varepsilon+\delta_t^\varepsilon+\delta^\varepsilon =-u_t^\varepsilon+\varepsilon^\alpha\dot W_2&\text{on}\;\partial D \\ \delta_t^\varepsilon =\frac{\partial u^\varepsilon}{\partial\mathrm n}&\text{on}\;\partial D \end{cases}NEWLINE\]NEWLINE with \(D\subset\mathbb R^3\) bounded and \(\alpha\geq1/2\), for~\(\varepsilon\) tending to zero.NEWLINENEWLINEDepending on \(\alpha<1\) or \(\alpha>1\), resp., limiting equations are identified as stochastic parabolic equations or as deterministic wave equations, respectively. For arbitrary \(\alpha\geq1/2\), convergence in distribution to a deterministic parabolic equation is obtained.