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Random attractors for stochastic semi-linear degenerate parabolic equations. (English) Zbl 1222.35042
Summary: The existence of a random attractor is established for a class of stochastic semi-linear degenerate parabolic equations with the leading term of the form \(\text{div}(\sigma (x)\nabla u)\) and additive spatially distributed temporal noise. The nonlinearity is dissipative for large values of the state without restriction on the growth order of the polynomial, while the spatial domain is either bounded or unbounded.

35B41 Attractors
35L55 Higher-order hyperbolic systems
35K58 Semilinear parabolic equations
35R60 PDEs with randomness, stochastic partial differential equations
35K65 Degenerate parabolic equations
Full Text: DOI
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