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Perturbations singulières de problèmes aux limites, non linéaires, «paraboliques dégénérés-hyperboliques»

Marie-Josée Jasor — 1998

Annales de la Faculté des sciences de Toulouse : Mathématiques

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

Marie-Josée Jasor; Laurent Lévi — 2003

Annales mathématiques Blaise Pascal

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 $ℝ^{p}$ , $1 \leq p < + \infty$ . 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.

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