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

Marie-Josée JasorLaurent 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 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.

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