The Existence Of Global Solutions To The Shock Diffraction Problems For Chaplygin Gas

In this thesis,we study the existence and regularity of the global solutions to the shock diffraction problems by wedges,modeled by isentropic and irrotational Euler equations with Chaplygin gas state.When the planar shock passes a convex cornered wedge,it will intersect with the wedge.The shock diffraction problem can be reduced to a free boundary problem for nonlinear partial differential equations of mixed type.These equations are hyperbolic in supersonic domain,while elliptic in subsonic domain.The mixed type equation is one of the hot topics in partial differential equations,which has many important applications.This thesis is organized as follows.Chapter One is an introduction.It is devoted to introducing the physical background and current research works on Chaplygin gas and shock diffraction by wedges.In Chapter Two,we introduce the basic properties of Chaplygin gas and the known results of the one-dimensional Riemann problem for Chaplygin gas.In Chapter Three,we study the interaction of shock waves after the planar shock passes through convex cornered wedges,as well as the global existence and regularity of solutions.We discuss the problem in three cases: the incoming flow is subsonic,sonic and supersonic.