%0 Journal Article
%T On quasilinear parabolic evolution equations in weighted $L_p$-spaces
%A Matthias K£¿hne
%A Jan Pruess
%A Mathias Wilke
%J Mathematics
%D 2009
%I arXiv
%X 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 $\om$-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.
%U http://arxiv.org/abs/0909.1480v1