Carrillo Menéndez, José2023-06-202023-06-201998-07Bardos C., Leroux A.Y., NCdClec J.-C., First order quasilinear equations with boundary conditions, Commun. Partial Differ. Eq. 4 (9) (1979) 1017-1034. BCnilan Ph., Equations d’evolution dans un espace de Banach quelconque et applications, These d’Etat, Orsay, 1972. BCnilan Ph., Tome H., Sur J’equation generale r,,r = (P(~L),~ -$(?I)., +v, C. R. Acad. Sci. Paris t. 299 SCrie I (1984) 919-922. Canillo J., Entropy solutions of nonlinear degenerate problems (a paraitre). Kruzhkov S.N., Generalized solutions of the Cauchy problem in the large for non-linear equations of first order, Dokl. Akad. Nauk SSSR 187 (1) (1969) 29-32. (English transl.: Soviet Math. Dokl. 10 (1969).) Kruzhkov S.N., First order quasilinear equations in several independent variables, Mat. Sbomik 81 (2) (1970) 228-255. (English transl.: Math. USSR Sb. 10 (1970)) Oleinik O.A., On the equations of unsteady filtration type, Uspekhi Mat. Nauk 12 (1957) 3-73.0764-444210.1016/S0764-4442(98)80009-8https://hdl.handle.net/20.500.14352/57351Contiene una versión abreviada del artículo original publicado en Arch. Rational Mech. Anal. 147 (1999) 269-361We consider a class of elliptic-hyperbolic degenerate equations g(u) - Delta b(u) + div phi(u) = f With Dirichlet homogeneous boundary conditions, and a class of elliptic-parabolic-hyperbolic degenerate equations g(u)(t) - Delta b(u) + div phi(u) = f with homogeneous Dirichlet conditions and initial conditions. The existence and uniqueness of entropy solutions for both problems are proved for nondecreasing continuous functions g and b vanishing at zero, and for continuous vectorial function satisfying rather general conditions.engjournal articlehttp://www.sciencedirect.com/science/article/pii/S0764444298800098http://www.sciencedirect.com/restricted access517.9Parabolic equationsEcuaciones diferenciales1202.07 Ecuaciones en Diferencias