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$%A. Plouvier, Sur
une classe de problèmes d’évolution quasi linéaires dégénérés, Rev. Mat. Univ. Complut. Madrid
8 (1995), no. 1, 197–227.%$
We are concerned with the existence, uniqueness and qualitative behavior of weak solutions to nonlinear conservation laws, of the form
associated with mixed conditions on the parabolic boundary. We establish a global result of existence for initial data in the space , when coefficients of are Carathéodory functions.
Under these assumptions, we prove the global uniqueness with additional information on the structure of the matrix of absolute permeability . The asymptotic behavior of the solution and the local hyperbolic character of the degenerate equation are specified.
1991 Mathematics Subject Classification: 35K55, 35J60, 58G11.