Entropy Solutions for Nonlinear Degenerate Problems
- Cite this article as:
- Carrillo, J. Arch Rational Mech Anal (1999) 147: 269. doi:10.1007/s002050050152
- 602 Downloads
. We consider a class of elliptic‐hyperbolic degenerate equations \(g(u)-\Delta b(u) +\divg\phi (u) =f\) with Dirichlet homogeneous boundary conditions and a class of elliptic‐parabolic‐hyperbolic degenerate equations \(g(u)_t-\Delta b(u) +\divg\phi (u) =f\) with homogeneous Dirichlet conditions and initial conditions. Existence of entropy solutions for both problems is proved for nondecreasing continuous functions g and b vanishing at zero and for a continuous vectorial function φ satisfying rather general conditions. Comparison and uniqueness of entropy solutions are proved for g and b continuous and nondecreasing and for φ continuous.