Global attractors for a class of degenerate parabolic equations with memory. (English) Zbl 1503.35043
Weighted equations which contain a degenerated term with the weighted coefficient \(a(x)\) and a memory term in a bounded domain \(\Omega\) with smooth boundary \(\partial\Omega\) are considered in this paper. The authors first investigate the existence and uniqueness of weak solutions to the initial-boundary value problem of the above-mentioned equation under suitable assumptions on the weight function \(a(x)\). Based on the existence and uniqueness of weak solutions, the existence of a global attractor is obtained. The main contribution of this paper is to extend some known results to cases with memory.
Reviewer: Pengyu Chen (Lanzhou)
MSC:
| 35B41 | Attractors |
| 35D30 | Weak solutions to PDEs |
| 35K20 | Initial-boundary value problems for second-order parabolic equations |
| 35K58 | Semilinear parabolic equations |
| 35K65 | Degenerate parabolic equations |
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