Pullback attractors for a non-autonomous semilinear degenerate parabolic equation. (English) Zbl 1368.35162
Summary: In this paper, we consider the pullback attractors for a nonautonomous semilinear degenerate parabolic equation \(u_t-\text{div}(\sigma(x)\nabla u)+ f(u)= g(x, t)\) defined on a bounded domain \(\Omega\subset\mathbb{R}^N\) with smooth boundary. We provide that the usual \((L^2(\Omega),L^2(\Omega))\) pullback \({\mathcal D}_\lambda\)-attractor indeed can attract the \({\mathcal D}_\lambda\)-class in \(L^{2+\delta}(\Omega)\), where \(\delta\in[0,\infty)\) can be arbitrary.
MSC:
35K65 | Degenerate parabolic equations |
35B40 | Asymptotic behavior of solutions to PDEs |
35B41 | Attractors |
35K58 | Semilinear parabolic equations |