Attractors for a damped stochastic wave equation of sine-Gordon type with sublinear multiplicative noise. (English) Zbl 1103.37053
Summary: The existence of compact random attractors is proved for a damped stochastic wave equation of sine-Gordon type with sublinear multiplicative noise under homogeneous Dirichlet boundary condition. To be important, in this note a precise estimate of upper bound of Hausdorff dimension of the random attractors is obtained in lower dimension.
MSC:
37L55 | Infinite-dimensional random dynamical systems; stochastic equations |
37L30 | Attractors and their dimensions, Lyapunov exponents for infinite-dimensional dissipative dynamical systems |
35Q53 | KdV equations (Korteweg-de Vries equations) |
35B41 | Attractors |
35L70 | Second-order nonlinear hyperbolic equations |
35R60 | PDEs with randomness, stochastic partial differential equations |
60H15 | Stochastic partial differential equations (aspects of stochastic analysis) |
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