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

Jasor, Marie-Josée; Lévi, Laurent

Annales mathématiques Blaise Pascal, Tome 10 (2003) no. 2, pp. 269-296.

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 ${ℝ}^p$, $1\le p<+\infty$. 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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