Workshop
Global existence and explosion of the stochastic viscoelastic wave equation driven by multiplicative noises
- Liang Fei (Xi'an + FSU Jena)
Abstract
We discuss an initial boundary value problem of stochastic viscoelastic wave equation driven by multiplicative noise involving the nonlinear damping term $|u_t|^{q-2}u_t$ and a source term of the type $|u|^{p-2}u$. We firstly establish the local existence and uniqueness of solution by the iterative technique truncation function method. Moreover, we also show that the solution is global for $q\geq p$. Lastly, by modifying the energy functional, we give sufficient conditions such that the local solution of the stochastic equations will blow up with positive probability or explode in energy sense for $p>q$.