Existence And Blow-up Of Weak Solution To Elliptic-hyperbolic-hyperbolic Type Of A Generalized Davey-stewartson System

In this paper, we study the Cauchy problem of the following two-dimensional generalized Davey-Stewartson system:This system is a Schrodinger equation coupled with two hyperbolic equations, which is often called elliptic-hyperbolic-hyperbolic Davey-Stewartson system. In this paper We state the existence and blow-up of weak solutions of equations.The contents of this paper is as follows:In the first chapter, we introduce the research significance and the research back-ground, and some research results of this paper.In the second chapter, we give the main preparatory knowledge needed in the process of the main result proving, including basic mark, basic lemma involved in this paper.In the third chapter, we prove the existence of weak solution to the system inIn the fourth chapter, we prove the weak solutions will blow up in H1(R2) under certain conditions.