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Semi-classical solutions for a nonlinear coupled elliptic-parabolic problem

Published online by Cambridge University Press:  17 April 2009

Catherine Choquet
Catherine Choquet
Affiliation:
LATP, CNRS UMR 6632, Université Paul Cézanne (Aix-Marseille III), FST, Case Cour 13397 Marseille Cedex 20, France e-mail: c.choquet@univ-cezanne.fr
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We give an existence result for a fully nonlinear system consisting of a parabolic equation strongly coupled with an elliptic one. It models in particular miscible displacement in porous media. To this aim, we adapt the tools of Ladyzenskaja, Solon-nikov and Uralćeva [27, 28] to the coupled nonlinear setting. Under some reasonable assumptions on the data, we state the existence of semi-classical solutions for the problem. We also give an existence result of weak solutions for a degenerate form of the problem.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 76 , Issue 3 , December 2007 , pp. 369 - 396
Copyright
Copyright © Australian Mathematical Society 2007

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