On a nonlinear degenerate parabolic transport-diffusion equation with a discontinuous coefficient.

Karlsen, Kenneth H.; Risebro, Nils H.; Towers, John D.

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Existence of solutions for nonlinear parabolic systems via weak convergence of truncations.

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

Marie-Josée Jasor, Laurent Lévi (2003)

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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 $ℝ^{p}$ , $1 \leq p < + \infty$ . 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.