The Error Estimate For A Special Nonlinear Degenerate Parabolic-hyperbolic Equation

This paper focuses on the error estimates a class of nonlinear degenerateparabolic hyperbolic equation.The paper first describes the deterioration parabolic physical model of hy-perbolic equations to two-phase boundary layer, we detailed the derivation of thePrandtl boundary layer equations, which is a typical of anisotropic degenerateparabolic hyperbolic equations.In the second chapter we introduced the present situation of the second-ordernonlinear degenerate parabolic hyperbolic equation, generalized and compared theresearch results for the isotropic and anisotropic, Cauchy problem and Dirichletboundary value problems . Next, we introduced error estimates of the conserva-tion law equation , primarily using the Kuznetsov approximation theory and theimproved method of Cockburn and others , which is also our source to do errorestimation for degenerate parabolic hyperbolic equations. In Chapter Three, we in-troduced the the definition of entropy solutions of degenerate parabolic hyperbolicequation , proposed the main theorem and proved it.