Singularity Formation Of Compressible Euler Equations With Source

In this paper,we mainly study the singularities of the compressible Euler equations and p-system with source where x is the space variable,t ? R+[0,?)is the time variable.This paper is divided into three chapters.In chapter one,we firstly introduce the physical background and significance of the related equations.Secondly,we introduce the Euler coordinate system and the Lagrange coordinate system,we also give the transformation of the equations under these two coordinate systems.Finally,we introduce the domestic and foreign research on singularity formation of compressible Euler equations and the content of this paper.In chapter two,we study the singularity formation of the solution on compressible Euler equations with source,we discussed separately the case of source term for Riemann invariants function and Riemann invariants.In chapter three,the singularity of p-system with source is studied,and the case of the source for Riemann invariants and the Rie-mann invariants function is discussed respectively,meanwhile we given the lower bound of the density.