Existence, uniqueness, and energy of modified stochastic sine-Gordon equation with multiplicative noise on one-dimensional domain

DOI10.1090/conm/668/13406zbMath1415.60079OpenAlexW4243238819MaRDI QIDQ5225289

Henri Schurz, Abdallah M. Talafha

Publication date: 19 July 2019

Published in: Probability on Algebraic and Geometric Structures (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/conm/668/13406

zbMATH Keywords

stabilityLyapunov functionalexpected energyFourier solutionadditive and multiplicative space-time noisemodified stochastic sine-Gordon equation

Mathematics Subject Classification ID

Stochastic ordinary differential equations (aspects of stochastic analysis) (60H10) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Applications of stochastic analysis (to PDEs, etc.) (60H30) Stochastic partial differential equations (aspects of stochastic analysis) (60H15) Generation, random and stochastic difference and differential equations (37H10) PDEs with randomness, stochastic partial differential equations (35R60)

Cites Work

• Existence and uniqueness of solutions of semilinear stochastic infinite-dimensional differential systems with \(H\)-regular noise
• Infinite-dimensional dynamical systems in mechanics and physics
• The stochastic wave equation in two spatial dimensions
• Random attractor for a damped sine-Gordon equation with white noise
• A stochastic wave equation in two space dimensions: smoothness of the law
• Stochastic wave equations with cubic nonlinearity and Q-regular additive noise in \(\mathbb R^2\)
• STOCHASTIC WAVE EQUATIONS WITH NONLINEAR DAMPING AND SOURCE TERMS
• Stochastic Equations in Infinite Dimensions
• Attractors for a Damped Stochastic Wave Equation of Sine–Gordon Type with Sublinear Multiplicative Noise
• Stochastic differential equations. An introduction with applications.
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