Full paper in PDF:
$%A. Plouvier, Sur une classe de problèmes d’évolution quasi linéaires dégénérés, Rev. Mat. Univ. Complut. Madrid 8 (1995), no. 1, 197–227.%$

Sur une classe de problèmes d’évolution quasi linéaires dégénérés
Anne PLOUVIER
Université de Pau & CNRS
Laboratoire de Mathématiques Appliquées
U.A. 1204 - CNRS
Avenue de l’Université
64000 Pau — France

Received: May 28, 1993
ABSTRACT

We are concerned with the existence, uniqueness and qualitative behavior of weak solutions to nonlinear conservation laws, of the form

@u- ' ' @t -div(A(.,u) \~/ f(u))= 0, f(0) =f (0)= 0, f > 0,

associated with mixed conditions on the parabolic boundary. We establish a global result of existence for initial data in the space L oo , when coefficients of A are Carathéodory functions.

Under these assumptions, we prove the global uniqueness with additional information on the structure of the matrix of absolute permeability A(.,.) . The asymptotic behavior of the solution and the local hyperbolic character of the degenerate equation are specified.

1991 Mathematics Subject Classification: 35K55, 35J60, 58G11.