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Entropy solutions for nonlinear degenerate problems. (Solutions entropiques de problèmes non linéaires dégénérés.) (French. Abridged English version) Zbl 0915.35026
Summary: We consider a class of elliptic-hyperbolic degenerate equations $$g(u)- \Delta b(u)+ \text{div }\phi(u)= f$$ with Dirichlet homogeneous boundary conditions, and a class of elliptic-parabolic-hyperbolic degenerate equations $$g(u)_t- \Delta b(u)+ \text{div }\phi(u)= f$$ 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 $$\phi$$ satisfying rather general conditions.

##### MSC:
 35D05 Existence of generalized solutions of PDE (MSC2000) 35M10 PDEs of mixed type 35J70 Degenerate elliptic equations 35K65 Degenerate parabolic equations 35L80 Degenerate hyperbolic equations
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