The homogeneous dirichlet problem for quasilinear anisotropic degenerate parabolic-hyperbolic equation with L initial value

The aim of this paper is to prove the well-posedness (existence and uniqueness) of the L^p entropy solution to the homogeneous Dirichlet problems for the anisotropic degenerate parabolic-hyperbolic equations with L^p initial value. We use the device of doubling variables and some technical analysis to prove the uniqueness result. Moreover we can prove that the L^p entropy solution can be obtained as the limit of solutions of the corresponding regularized equations of nondegenerate parabolic type.