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Title: Local existence, uniqueness, and smooth dependence for nonsmooth quasilinear parabolic problems
Authors: Griepentrog, Jens AndréRecke, Lutz
Issue Date: 2009
Published in: Preprint / Weierstraß-Institut für Angewandte Analysis und Stochastik im Forschungsverbund Berlin e.V. , Volume 1409, ISSN 0946-8633
Publisher: Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik
Abstract: A general theory on local existence, uniqueness, regularity, and smooth dependence in Hölder spaces for a general class of quasilinear parabolic initial boundary value problems with nonsmooth data has been developed. As a result the gap between low smoothness of the data, which is typical for many applications, and high smoothness of the solutions, which is necessary for the applicability of differential calculus to the abstract formulations of the initial boundary value problems, has been closed. The main tools are new maximal regularity results of the first author in Sobolev-Morrey spaces, linearization techniques and the Implicit Function Theorem. Typical applications are transport processes of charged particles in semiconductor heterostructures, phase separation processes of nonlocally interacting particles, chemotactic aggregation in heterogeneous environments as well as optimal control by means of quasilinear elliptic and parabolic PDEs with nonsmooth data.
Keywords: Sobolev–Morrey spaces; maximal regularity; Implicit Function Theorem; sets with Lipschitz boundary; mixed boundary conditions.
DDC: 510
License: This document may be downloaded, read, stored and printed for your own use within the limits of § 53 UrhG but it may not be distributed via the internet or passed on to external parties.
Dieses Dokument darf im Rahmen von § 53 UrhG zum eigenen Gebrauch kostenfrei heruntergeladen, gelesen, gespeichert und ausgedruckt, aber nicht im Internet bereitgestellt oder an Außenstehende weitergegeben werden.
Appears in Collections:Mathematik

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