Homogeneous Dirichlet problems for quasilinear anisotropic degenerate parabolic–hyperbolic equations

The aim of this paper is to prove the well-posedness (existence and uniqueness) of entropy solutions to the general anisotropic degenerate parabolic–hyperbolic equations with L∞ initial data and homogeneous Dirichlet boundary condition. We use the doubling variables device to prove a comparison theorem, which implies the uniqueness. The existence of entropy solutions can be obtained by finding the limit of solutions for the regularized equation of strictly parabolic type.