RENORMALIZED ENTROPY SOLUTIONS OF HOMOGENEOUS DIRICHLET PROBLEMS FOR QUASILINEAR ANISOTROPIC DEGENERATE PARABOLIC-HYPERBOLIC EQUATIONS

摘要

We study the well-posedness of renormalized entropy solutions for quasilinear anisotropic degenerate parabolic-hyperbolic equation of the type ?_tu+divf(u) = ▽· (a(uu)▽u) in a bounded domain with general L~1 initial data and homogeneous Dirichlet boundary condition. We use the device of doubling variables to prove the uniqueness and use the vanishing viscosity method to prove the existence.