Maximal regularity for a free boundary problem

verfasst von

Joachim Escher, Gieri Simonett

Abstract

This paper is concerned with the motion of an incompressible fluid in a rigid porous medium of infinite extent. The fluid is bounded below by a fixed, impermeable layer and above by a free surface moving under the influence of gravity. The laminar flow is governed by Darcy's law. We prove existence of a unique maximal classical solution, using methods from the theory of maximal regularity, analytic semigroups, and Fourier multipliers. Moreover, we describe a state space which can be considered as domain of parabolicity for the problem under consideration.

Externe Organisation(en)

Universität Basel
Vanderbilt University

Typ

Artikel

Journal

Nonlinear Differential Equations and Applications NoDEA

Band

2

Seiten

463-510

Anzahl der Seiten

48

ISSN

1021-9722

Publikationsdatum

12.1995

Publikationsstatus

Veröffentlicht

Peer-reviewed

Ja

ASJC Scopus Sachgebiete

Analysis, Angewandte Mathematik

Elektronische Version(en)

https://doi.org/10.1007/BF01210620 (Zugang: Unbekannt)