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Dynamical behavior for stochastic wave equation with nonlinear damping and white noise on unbounded domains. (Chinese. English summary) Zbl 1449.35075

Summary: The existence of random attractor for stochastic non-autonomous wave equation with nonlinear damping and additive noise on unbounded domains is studied. By using the uniform estimates of solutions of transformed system and the decomposition technique on the space, the existence of asymptotically compact \(\mathcal{D}\)-pullback absorbing set is obtained, and then the existence of random attractor of original system is given.

MSC:

35B40 Asymptotic behavior of solutions to PDEs
35B41 Attractors
35L05 Wave equation
35R60 PDEs with randomness, stochastic partial differential equations
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