Obstacle problems for scalar conservation laws

Laurent Levi

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique (2001)

  • Volume: 35, Issue: 3, page 575-593
  • ISSN: 0764-583X

Abstract

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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.

How to cite

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Levi, Laurent. "Obstacle problems for scalar conservation laws." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 35.3 (2001): 575-593. <http://eudml.org/doc/194063>.

@article{Levi2001,
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^\infty $. Lastly, we study the behaviour of this solution and its stability properties with respect to the associated obstacle functions.},
author = {Levi, Laurent},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},
keywords = {obstacle problem; conservation laws; entropy solution; bilateral obstacle problem; Dirichlet boundary conditions; penalization method},
language = {eng},
number = {3},
pages = {575-593},
publisher = {EDP-Sciences},
title = {Obstacle problems for scalar conservation laws},
url = {http://eudml.org/doc/194063},
volume = {35},
year = {2001},
}

TY - JOUR
AU - Levi, Laurent
TI - Obstacle problems for scalar conservation laws
JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
PY - 2001
PB - EDP-Sciences
VL - 35
IS - 3
SP - 575
EP - 593
AB - 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^\infty $. Lastly, we study the behaviour of this solution and its stability properties with respect to the associated obstacle functions.
LA - eng
KW - obstacle problem; conservation laws; entropy solution; bilateral obstacle problem; Dirichlet boundary conditions; penalization method
UR - http://eudml.org/doc/194063
ER -

References

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