Obstacle problems for scalar conservation laws
ESAIM: Modélisation mathématique et analyse numérique, Tome 35 (2001) no. 3, pp. 575-593.

Ce travail a pour objet l’étude de problèmes d’obstacles bilatéraux pour des lois de conservation scalaires quasi-linénaires du premier ordre associées à des conditions aux limites de Dirichlet. On donne d’abord une formulation entropique qui garantit l’unicité. On justifie alors l’existence d’une solution par utilisation de la méthode de pénalisation et au moyen de la notion de processus entropique solution due aux propriétés des suites bornées dans L ∞ . Enfin, on étudie le comportement de cette solution et ses propriétés de stabilité en fonction des contraintes d’obstacle associées.

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.

Classification : 35L65, 35R35, 35L85
Mots-clés : obstacle problem, conservation laws, entropy solution 
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Levi, Laurent. Obstacle problems for scalar conservation laws. ESAIM: Modélisation mathématique et analyse numérique, Tome 35 (2001) no. 3, pp. 575-593. http://archive.numdam.org/item/M2AN_2001__35_3_575_0/

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