Existence And Decay Of Weak Solution To Elliptic-hyperbolic-hyperbolic Type Of A Generalized Davey-stewartson Systems

The Davey-Stewartson systems describe the evolution of weakly nonlinear water waves that travel predominantly in one direction, but in which the wave amplitude is modulated slowly in two horizontal directions. They have also important applications in plasma physics, ferromagnetic physics and other fields.In this thesis, we discuss the Cauchy problem of the following three-component 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. We study the existence and decay of weak solutions in weighted space H1,0(R2) and H0,1(R2), whereThe first chapter is an introduction. We state the background and the research results related to this thesis.In the second chapter, we give the main preparatory knowledge needed in the process of proving the main results.In Chapter Three, we study the global existence of weak solutions to the Cauchy problem of the above generalized elliptic-hyperbolic-hyperbolic type Davey-Stewartson system in weighted space H1,0(R2),H0,1(R2).In Chapter Four, we prove the decay of weak solutions to the above generalized Davey-Stewartson system in Lp(R2) for p>2.