# Obstacle problems for scalar conservation laws

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

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topLevi, 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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