Singular Perturbations for a Class of Degenerate Parabolic Equations with Mixed Dirichlet-Neumann Boundary Conditions

Marie-Josée Jasor[1]; Laurent Lévi[2]

  • [1] Université Blaise Pascal Laboratoire de Mathématiques Appliquées UMR 6620 CNRS 24 avenue des Landais 63117 Aubiere Cedex FRANCE
  • [2] Université de Pau Laboratoire de Mathématiques Appliquées ERS 2055 CNRS BP 1155 64013 Pau Cedex FRANCE

Annales mathématiques Blaise Pascal (2003)

  • Volume: 10, Issue: 2, page 269-296
  • ISSN: 1259-1734

Abstract

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We establish a singular perturbation property for a class of quasilinear parabolic degenerate equations associated with a mixed Dirichlet-Neumann boundary condition in a bounded domain of ℝ p , 1 ≤ p < + ∞ . In order to prove the L 1 -convergence of viscous solutions toward the entropy solution of the corresponding first-order hyperbolic problem, we refer to some properties of bounded sequences in L ∞ together with a weak formulation of boundary conditions for scalar conservation laws.

How to cite

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Jasor, Marie-Josée, and Lévi, Laurent. "Singular Perturbations for a Class of Degenerate Parabolic Equations with Mixed Dirichlet-Neumann Boundary Conditions." Annales mathématiques Blaise Pascal 10.2 (2003): 269-296. <http://eudml.org/doc/10490>.

@article{Jasor2003,
abstract = {We establish a singular perturbation property for a class of quasilinear parabolic degenerate equations associated with a mixed Dirichlet-Neumann boundary condition in a bounded domain of $\mathbb\{R\}^p$, $1 \le p &lt;+\infty $. In order to prove the $L^1$-convergence of viscous solutions toward the entropy solution of the corresponding first-order hyperbolic problem, we refer to some properties of bounded sequences in $L^\infty $ together with a weak formulation of boundary conditions for scalar conservation laws.},
affiliation = {Université Blaise Pascal Laboratoire de Mathématiques Appliquées UMR 6620 CNRS 24 avenue des Landais 63117 Aubiere Cedex FRANCE; Université de Pau Laboratoire de Mathématiques Appliquées ERS 2055 CNRS BP 1155 64013 Pau Cedex FRANCE},
author = {Jasor, Marie-Josée, Lévi, Laurent},
journal = {Annales mathématiques Blaise Pascal},
keywords = {existence and uniqueness theorem; first-order hyperbolic equation; entropy solution},
language = {eng},
month = {7},
number = {2},
pages = {269-296},
publisher = {Annales mathématiques Blaise Pascal},
title = {Singular Perturbations for a Class of Degenerate Parabolic Equations with Mixed Dirichlet-Neumann Boundary Conditions},
url = {http://eudml.org/doc/10490},
volume = {10},
year = {2003},
}

TY - JOUR
AU - Jasor, Marie-Josée
AU - Lévi, Laurent
TI - Singular Perturbations for a Class of Degenerate Parabolic Equations with Mixed Dirichlet-Neumann Boundary Conditions
JO - Annales mathématiques Blaise Pascal
DA - 2003/7//
PB - Annales mathématiques Blaise Pascal
VL - 10
IS - 2
SP - 269
EP - 296
AB - We establish a singular perturbation property for a class of quasilinear parabolic degenerate equations associated with a mixed Dirichlet-Neumann boundary condition in a bounded domain of $\mathbb{R}^p$, $1 \le p &lt;+\infty $. In order to prove the $L^1$-convergence of viscous solutions toward the entropy solution of the corresponding first-order hyperbolic problem, we refer to some properties of bounded sequences in $L^\infty $ together with a weak formulation of boundary conditions for scalar conservation laws.
LA - eng
KW - existence and uniqueness theorem; first-order hyperbolic equation; entropy solution
UR - http://eudml.org/doc/10490
ER -

References

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