Random attractors for stochastic parabolic equations with additive noise in weighted spaces. (English) Zbl 1516.35106
Summary: In this paper, we establish the existence of random attractors for stochastic parabolic equations driven by additive noise as well as deterministic non-autonomous forcing terms in weighted Lebesgue spaces \(L_{\delta}^r(\mathcal{O})\), where \(1<r<\infty\), \(\delta\) is the distance from \(x\) to the boundary. The nonlinearity \(f(x,u)\) of equation depending on the spatial variable does not have the bound on the derivative in \(u\), and then causes critical exponent. In both subcritical and critical cases, we get the well-posedness and dissipativeness of the problem under consideration and, by smoothing property of heat semigroup in weighted space, the asymptotical compactness of random dynamical system corresponding to the original system.
MSC:
| 35B41 | Attractors |
| 35R60 | PDEs with randomness, stochastic partial differential equations |
| 37B55 | Topological dynamics of nonautonomous systems |
| 37L30 | Attractors and their dimensions, Lyapunov exponents for infinite-dimensional dissipative dynamical systems |
| 37L05 | General theory of infinite-dimensional dissipative dynamical systems, nonlinear semigroups, evolution equations |
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