Displaying similar documents to “On second order nonlinear equations with rectilinear characteristics.”

On the well posedness of vanishing viscosity limits

Alberto Bressan (2002)

Journées équations aux dérivées partielles

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This paper provides a survey of recent results concerning the stability and convergence of viscous approximations, for a strictly hyperbolic system of conservation laws in one space dimension. In the case of initial data with small total variation, the vanishing viscosity limit is well defined. It yields the unique entropy weak solution to the corresponding hyperbolic system.

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

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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.