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On quasilinear parabolic evolution equations in weighted L p -spaces |
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| Authors: | Matthias Köhne Jan Prüss Mathias Wilke |
| Institution: | 1. Center for Smart Interfaces and International, Research Training Group “Mathematical, Fluid Dynamics”, Technical University Darmstadt, Petersenstr. 32, 64287, Darmstadt, Germany 2. Institut für Mathematik, Martin-Luther-Universit?t Halle-Wittenberg, Theodor-Lieser-Str. 5, 06120, Halle, Germany 3. Institut für Mathematik, Martin-Luther-Universit?t Halle-Wittenberg, Theodor-Lieser-Str. 5, 06120, Halle, Germany |
| Abstract: | In this paper we develop a geometric theory for quasilinear parabolic problems in weighted L p -spaces. We prove existence and uniqueness of solutions as well as the continuous dependence on the initial data. Moreover, we make use of a regularization effect for quasilinear parabolic equations to study the ω-limit sets and the long-time behaviour of the solutions. These techniques are applied to a free boundary value problem. The results in this paper are mainly based on maximal regularity tools in (weighted) L p -spaces. |
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