×

zbMATH — the first resource for mathematics

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
PDF BibTeX XML Cite
Full Text: DOI