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Obstacle problems for scalar conservation laws

Published online by Cambridge University Press:  15 April 2002

Laurent Levi
Laurent Levi*
Affiliation:
University of Pau, CNRS, Laboratory of Applied Mathematics ERS 2055, I.P.R.A., Avenue de l'Université, 64000 Pau, France. ([email protected])
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Abstract

In this paper we are interested in bilateral obstacle problems for quasilinear scalar conservation laws associated with Dirichlet boundary conditions. Firstly, we provide a suitable entropy formulation which ensures uniqueness. Then, we justify the existence of a solution through the method of penalization and by referring to the notion of entropy process solution due to specific properties of bounded sequences in L ∞. Lastly, we study the behaviour of this solution and its stability properties with respect to the associated obstacle functions.

Keywords

Obstacle problemconservation lawsentropy solution.
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 35 , Issue 3 , May 2001 , pp. 575 - 593
Copyright
© EDP Sciences, SMAI, 2001

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