Stochastic wave equations with cubic nonlinearity and Q-regular additive noise in $\mathbb{R}^2$

Semi-linear wave equations on rectangular domains in $\mathbb{R}^2$ (vibrating plates) with certain cubic quasi-nonlinearities and perturbed by a Q-regular space-time white noise are considered analytically. These models as 2nd order SPDEs (stochastic partial differential equations) with non-random Dirichlet- type boundary conditions describe the displacement of noisy vibrations of rectangular plates as met in engineering. We discuss their analysis by the eigen- function approach allowing us to truncate the infinite-dimensional stochastic systems (i.e. the SDEs of Fourier coefficients related to semilinear SPDEs), to control its energy, existence, uniqueness, continuity and stability. A conservation law for at most linearly growing expected energy is established in terms of system-parameters.