Stochastic wave equations with cubic nonlinearity and Q-regular additive noise in R 2
Henri Schurz · AIMS Press eBooks · 2011
Semi-linear wave equations on rectangular domains in $\mathbb{R}^2$ (vibrating plates) with certain cubic quasi-nonlinearities and perturbed by a Q-regularspace-time white noise are considered analytically. These models as 2nd orderSPDEs (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 stochasticsystems (i.e. the SDEs of Fourier coefficients related to semilinear SPDEs), tocontrol its energy, existence, uniqueness, continuity and stability. A conservation law for at most linearly growing expected energy is established in termsof system-parameters.