Geodesic
Singular Perturbations for a Class of Degenerate Parabolic Equations with Mixed Dirichlet-Neumann Boundary Conditions
Jasor, Marie-Josée1  ; Lévi, Laurent2
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, Tome 10 (2003) no. 2, pp. 269-296

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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.

DOI : 10.5802/ambp.177

Jasor, Marie-Josée 1 ; Lévi, Laurent 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 
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     title = {Singular {Perturbations} for a {Class} of {Degenerate} {Parabolic} {Equations} with {Mixed} {Dirichlet-Neumann} {Boundary} {Conditions}},
     journal = {Annales math\'ematiques Blaise Pascal},
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Jasor, Marie-Josée; Lévi, Laurent. Singular Perturbations for a Class of Degenerate Parabolic Equations with Mixed Dirichlet-Neumann Boundary Conditions. Annales mathématiques Blaise Pascal, Tome 10 (2003) no. 2, pp. 269-296. doi: 10.5802/ambp.177

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