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New unilateral problems in stratigraphy

Published online by Cambridge University Press:  15 November 2006

Stanislav N. Antontsev ,
Gérard Gagneux ,
Robert Luce  and
Guy Vallet
Stanislav N. Antontsev
Affiliation:
Departamento de Matemática, Universidade da Beira Interior Covilhã 6201-001, Portugal. anton@ubi.pt
Gérard Gagneux
Affiliation:
Laboratoire de Mathématiques Appliquées UMR-CNRS 5142 IPRA  BP 1155, 64 013 Pau Cedex, France. gerard.gagneux@univ-pau.fr; robert.luce@univ-pau.fr; guy.vallet@univ-pau.fr
Robert Luce
Affiliation:
Laboratoire de Mathématiques Appliquées UMR-CNRS 5142 IPRA  BP 1155, 64 013 Pau Cedex, France. gerard.gagneux@univ-pau.fr; robert.luce@univ-pau.fr; guy.vallet@univ-pau.fr
Guy Vallet
Affiliation:
Laboratoire de Mathématiques Appliquées UMR-CNRS 5142 IPRA  BP 1155, 64 013 Pau Cedex, France. gerard.gagneux@univ-pau.fr; robert.luce@univ-pau.fr; guy.vallet@univ-pau.fr
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Abstract

This work deals with the study of some stratigraphic models for the formation of geological basins under a maximal erosion rate constrain. It leads to introduce differential inclusions of degenerated hyperbolic-parabolic type $0\in \partial _{t}u-div\{H(\partial _{t}u+E)\nabla u\}$, where H is the maximal monotonous graph of the Heaviside function and E is a given non-negative function. Firstly, we present the new and realistic models and an original mathematical formulation, taking into account the weather-limited rate constraint in the conservation law, with a unilateral constraint on the outflow boundary. Then, we give a study of the 1-D case with numerical illustrations.

Keywords

Stratigraphic modelsweather limiteddegenerated parabolic-hyperbolic conservation laws.
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 40 , Issue 4 , July 2006 , pp. 765 - 784
Copyright
© EDP Sciences, SMAI, 2006

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References

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