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On quasilinear parabolic evolution equations in weighted L^p-spaces

Köhne, M. and Prüss, J. and Wilke, M. (2010):
On quasilinear parabolic evolution equations in weighted L^p-spaces.
In: J. Evol. Equ., 10, pp. 443-463. Birkhäuser/Springer Basel AG, [Article]

Item Type: Article
Erschienen: 2010
Creators: Köhne, M. and Prüss, J. and Wilke, M.
Title: On quasilinear parabolic evolution equations in weighted L^p-spaces
Language: English
Journal or Publication Title: J. Evol. Equ.
Journal volume: 10
Publisher: Birkhäuser/Springer Basel AG
Divisions: Exzellenzinitiative
Exzellenzinitiative > Clusters of Excellence
04 Department of Mathematics
Zentrale Einrichtungen
Exzellenzinitiative > Clusters of Excellence > Center of Smart Interfaces (CSI)
04 Department of Mathematics > Mathematical Modelling and Analysis
Date Deposited: 23 Sep 2011 10:10
Identification Number: doi:10.1007/s00028-010-0056-0
Alternative Abstract:
Alternative abstract Language

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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