Existence, uniqueness, and stability of stochastic wave equation with cubic nonlinearities in two dimensions
DOI10.1016/j.jmaa.2014.04.011zbMath1318.60069OpenAlexW2057442961MaRDI QIDQ488521
Haziem M. Hazaimeh, Henri Schurz
Publication date: 26 January 2015
Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/j.jmaa.2014.04.011
moment stabilityadditive space-time noiseenergy Lyapunov functionalnonlinear stochastic wave equationsample path stabilitystrong Fourier series solution
Stochastic ordinary differential equations (aspects of stochastic analysis) (60H10) Sample path properties (60G17) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Stochastic partial differential equations (aspects of stochastic analysis) (60H15) PDEs with randomness, stochastic partial differential equations (35R60)
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Cites Work
- Existence and uniqueness of solutions of semilinear stochastic infinite-dimensional differential systems with \(H\)-regular noise
- Analysis and discretization of semi-linear stochastic wave equations with cubic nonlinearity and additive space-time noise
- Nonlinear stochastic wave equations: blow-up of second moments in \(L^{2}\)-norm
- The stochastic wave equation in two spatial dimensions
- A stochastic wave equation in two space dimensions: smoothness of the law
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- STOCHASTIC WAVE EQUATIONS WITH NONLINEAR DAMPING AND SOURCE TERMS
- Stochastic Equations in Infinite Dimensions
- Stochastic differential equations. An introduction with applications.
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