Stochastic Wave Equations with Nonlinear Damping and Source Terms

2011/04/17 by Hui Gao, Boling Guo, Gao, Hongjun +3
Computer Science · Engineering · Mathematics · #Advanced Mathematical Modeling in Engineering #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.1104.3279

openalex publication_date 2011/04/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we discuss an initial boundary value problem for the stochastic wave equation involving the nonlinear damping term |u_t|^q-2u_t and a source term of the type |u|^p-2u. We firstly establish the local existence and uniqueness of solution by the Galerkin approximation method and show that the solution is global for q≥ p. Secondly, by an appropriate energy inequality, the local solution of the stochastic equations will blow up with positive probability or explosive in energy sense for p>q.

Related

• Blow-up for the one dimensional stochastic wave equations
• On the approximation for singularly perturbed stochastic wave equations
• Nonlinear stochastic wave Equation driven by rough noise
• Non-existence results for stochastic wave equations in one dimension
• A remark on triviality for the two-dimensional stochastic nonlinear wave equation