Well-posedness Of Entropy Solutions For Dirichlet Boundary Value Problems Of Anisotropic Degenerate Parabolic-hyperbolic Equations

In this thesis,we study the well-posedness of the entropic solutions of initial bound-ary value problems for quasilinear degenerate parabolic-hyperbolic equations with non-homogeneous Dirichlet boundary conditions,which can be used to describe the transport process of pollutants and so on.These equations include four possibilities:hyperbolic con-servation law,isotropic,anisotropic and strict parabolic type.The studies of hyperbolic conservation law(complete degenerate case)and strict parabolic type(complete non-degenerate case)are relatively perfect.This thesis mainly considers anisotropic equation(isotropy is a special case of anisotropy).Inspired by Dirichlet boundary value problem of hyperbolic conservation law,we introduce the concept of"entropy-entropy flow triple”of degenerate parabolic-hyperbolic equation and give the definition of entropy solution.The contribution of this thesis is to give a reasonable explanation of boundary conditions.In chapter 3,we prove the comparison theorem with respective to the initial data and source term with doubling variables device,and then we obtain the uniqueness.In Chapter 4,we prove the existence of the entropy solution by using the vanishing viscosity method.