Random attractors for stochastic semi-linear degenerate parabolic equations

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 div(σ(x)∇u)div(σ(x)∇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.