On quasilinear parabolic evolution equations in weighted Lp-spaces
On quasilinear parabolic evolution equations in weighted Lp-spaces
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DOI：
10.1007/s00028-010-0056-0
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发表时间：
2009-09
影响因子：
1.4
通讯作者：
M. Köhne;J. Prüss;M. Wilke
中科院分区：
文献类型：
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作者：
M. Köhne;J. Prüss;M. Wilke
本文发展了加权Lp-空间中拟线性抛物问题的一个几何理论。我们证明了解的存在唯一性以及对初始值的连续依赖性。此外，我们利用拟线性抛物方程的正则化效应，研究了其解的ω-极限集和长时间行为。这些技术被应用到一个自由边值问题。本文的结果主要是基于（加权）Lp-空间中的极大正则性工具。
In this paper we develop a geometric theory for quasilinear parabolic problems in weightedLp-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 theω-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)Lp-spaces.