Well-posedness Of Entropy Solutions Of Homogeneous Dirichlet Initial Boundary Value Problems For Weakly Coupled Quasilinear Degenerate Parabolic-hyperbolic Equations

In this thesis,we consider the well-posedness of the entropy solutions of the homogeneous Dirichlet initial boundary value problems for a class of weakly coupled quasilinear degenerate parabolic-hyperbolic equations.We first introduce a class of physical back-grounds of this type of equations:the migration process of pollutants.Then introduces the research history and mathematical difficulties of quasilinear degenerate parabolic-hyperbolic equations.Because the system of equations may degenerate and for the bound-ary value problem,the existence of the boundary layer sequence has not yet been under-stood well.In the second chapter,we first introduce the(boundary)entropy-entropy flow triple,and give the definition of the entropy solution.In the third chapter,we use the doubling variables method to obtain the internal and global comparison principle respec-tively,and thus prove the uniqueness of the entropy solution.In the fourth chapter,we construct a strict parabolic equation system and obtain the existence of the approximate solution,and then prove that when the viscosity disappears,the approximate solution tends to the entropy solution,and thus completes the proof of the existence of the entropy solution.