Singularity Analysis For A Degenerate Parabolic System With Time-dependent Coefficients

In this paper,we study the singularity and global regularity for a degenerate parabolic system with time-dependent coefficients under Neumann boundary condition.Firstly,we establish the comparison principle of the weak solution.Using comparison principle and some differential inequalities,we then give the conditions of the global existence and blow-up of solution of the system.This paper is divided into 3 chapters with contents as follows.Chapter 1 is mainly about the developmental background and significance of research of degenerate parabolic equations.Chapter 2 is mainly about the basics of PDEs,such as definitions,comparison principles and some basic knowledge,which are for the singularity analysis of a degenerate parabolic system with time-dependent coefficients in the next chapter.In Chapter 3,we prove that the comparison principle still holds for the given system with the Neumann boundary conditions.We also give some conditions for the existence and blow-up of a global solution of the system,by means of the comparison principle and differential inequality.Then we compare previous late results with ours,which reveals the originality of our work.