Obstacle problems for scalar conservation laws
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 35 (2001) no. 3, p. 575-593

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.

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.

Classification:  35L65,  35R35,  35L85
Keywords: obstacle problem, conservation laws, entropy solution
@article{M2AN_2001__35_3_575_0,
     author = {Levi, Laurent},
     title = {Obstacle problems for scalar conservation laws},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
     publisher = {EDP-Sciences},
     volume = {35},
     number = {3},
     year = {2001},
     pages = {575-593},
     zbl = {0990.35096},
     mrnumber = {1837085},
     language = {en},
     url = {http://www.numdam.org/item/M2AN_2001__35_3_575_0}
}
Levi, Laurent. Obstacle problems for scalar conservation laws. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 35 (2001) no. 3, pp. 575-593. http://www.numdam.org/item/M2AN_2001__35_3_575_0/

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