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Long-time behaviour for porous medium equations with convection

Published online by Cambridge University Press:  14 November 2011

Ph. Laurençot  and
F. Simondon
Ph. Laurençot
Affiliation:
Institut Elie Cartan-Nancy, Université de Nancy I, BP 239, F-54506 Vandœuvre les Nancy cedex, France
F. Simondon
Affiliation:
Equipe de Mathématiques, CNRS URA 741, Université de Franche-Comté, F-25030 Besançon cedex, France
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Abstract

Long-time behaviour of solutions to porous medium equations with convection is investigated when the initial datum is a non-negative and integrable function on the real line. The long-time profile of the solutions is determined, and depends on whether the convective or the diffusive effect dominates for large times. Sharp temporal decay estimates are also provided.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 128 , Issue 2 , 1998 , pp. 315 - 336
Copyright
Copyright © Royal Society of Edinburgh 1998

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