A note on a parabolic equation with nonlinear dynamical boundary condition
Please always quote using this URN:urn:nbn:de:0296-matheon-10709
- We consider a semilinear parabolic equation subject to a nonlinear dynamical boundary condition that is related to the so-calles Wentzell boundary condition. First, we prove the existence and uniqueness of global solutions as well as the existence of a global attractor. Then we derive a suitable Lojasiewicz-Simon-type inequality to show the convergence of global solutions to single steady states as time tends to infinity under the assumption that the nonlinear terms $f$, $g$ are real analytic. Moreover, we provide an estimate for the convergence rate.
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| Author: | Jürgen Sprekels, Hao Wu |
|---|---|
| URN: | urn:nbn:de:0296-matheon-10709 |
| Referee: | Fredi Tröltzsch |
| Document Type: | Preprint, Research Center Matheon |
| Language: | English |
| Date of first Publication: | 2012/03/09 |
| Release Date: | 2012/03/09 |
| Tag: | Lojasiewicz-Simon inequality; convergence to equilibrium; dynamical boundary condition; global attractor; parabolic equation |
| Institute: | Weierstraß-Institut für Angewandte Analysis und Stochastik (WIAS) |
| MSC-Classification: | 35-XX PARTIAL DIFFERENTIAL EQUATIONS / 35Bxx Qualitative properties of solutions / 35B40 Asymptotic behavior of solutions |
| 35-XX PARTIAL DIFFERENTIAL EQUATIONS / 35Bxx Qualitative properties of solutions / 35B41 Attractors | |
| 35-XX PARTIAL DIFFERENTIAL EQUATIONS / 35Bxx Qualitative properties of solutions / 35B45 A priori estimates | |
| Preprint Number: | 949 |
