Non Homogeneous Systems Of Conservation Laws Of The Existence Of Global Solutions

It is an important model to study the mathematical theory of fluid mechanics in the hyperbolic conservation equations, global solutions of the research on it has important theoretical significance and application value. Due to the problem of nonlinear, there are not overall solutions for classical weak solutions, therefore it has become the problem that people cares. In 1965, the proposed scheme is important for the research of the global existence of solution. It generally applies only to study the small initial value problem, but now in many documents, have spread it to study the large early. For example, Nishia in 1968 to p equations for adiabatic case studies, as well as Ding Xia wow, Zhang Tong and others in 1973 on a special initial non adiabatic case research etc.The main method is the method of random access format points to establish difference scheme, and by the nature of the shock wave and rarefaction wave interactions prove the approximate solution of the total variation boundedness, compactness and obtained the approximate solution.. this paper is mainly on the basis of previous work, the overall weak solutions of nonhomogeneous hyperbolic conservation law is studied. The main idea is to use the generalized format on the nonhomogeneous problem into homogeneous problem, based on the homogeneous structure equation of the reference solution. The second is to prove the existence of solution. The main use of shock wave and rarefaction wave properties of some proof based on the extended format structure of the reference solution is full variation bounded. Finally according to the existence of global solutions of entropy solution definition and Helly theorem to derive nonlinear hyperbolic conservation equations.