Existence, uniqueness, and stability of Fourier series solutions of stochastic wave equations with cubic nonlinearities in 3D

DOI10.1016/j.na.2022.113169zbMath1504.35663OpenAlexW4308924660MaRDI QIDQ2105532

Qasim S. Alharbi, Henri Schurz

Publication date: 8 December 2022

Published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.na.2022.113169

zbMATH Keywords

Lyapunov functionalfinite-dimensional approximationnonlinear stochastic wave equationenergy trace formulaquasilinear SPDEapproximate Fourier series solutions

Mathematics Subject Classification ID

Stochastic ordinary differential equations (aspects of stochastic analysis) (60H10) Stability for nonlinear problems in mechanics (70K20) Nonlinear waves in solid mechanics (74J30) Stochastic methods (Fokker-Planck, Langevin, etc.) applied to problems in time-dependent statistical mechanics (82C31) Stochastic partial differential equations (aspects of stochastic analysis) (60H15) PDEs with randomness, stochastic partial differential equations (35R60) Computational methods for stochastic equations (aspects of stochastic analysis) (60H35) Stochastic mechanics (including stochastic electrodynamics) (81P20) Second-order semilinear hyperbolic equations (35L71)

Cites Work

• Existence, uniqueness, and stability of stochastic wave equation with cubic nonlinearities in two dimensions
• Undamped nonlinear beam excited by additive \(L^{2}\)-regular noise
• Existence and uniqueness of solutions of semilinear stochastic infinite-dimensional differential systems with \(H\)-regular noise
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• Stochastic differential equations. An introduction with applications
• Stochastic wave equations with cubic nonlinearity and Q-regular additive noise in \(\mathbb R^2\)
• Upper bounds on the rate of convergence of truncated stochastic infinite-dimensional differential systems with \(H\)-regular noise
• Invariant Gibbs measure evolution for the radial nonlinear wave equation on the 3d ball
• Stochastic Equations in Infinite Dimensions
• On a Formula Concerning Stochastic Differentials
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