The Singular Perturbed Problem For Quasi-linear Equation System

This dissertation is devoted to a very important equation system among differential equation systems------quasi-linear equation system, as isa important topic of equation system(especially when discussed shock wave solution), Often appear in such research fields as Hydrokinetics, the semiconductor establishes in physical theory ,Chemical reaction theory , project, Biology , Communication and Ecology etc. Many authors have studied on singularly perturbed problems of quasi-linear equation and system. Some study them by differential inequality , diagonal transformation and fixed point theorem, others study them by bound function method. But all has the certain deficiency, for example stronger limit conditions, the low order approximate and the narrower applicable scope. So it is necessary to devote to singularly perturbed problems of quasi-linear equation system further. From this it makes up the insufficiency which mentioned in front, namely not only may reduce few conditions, moreover also may open up the question applicable scope, and obtains the existence and local uniqueness of solution of this problem and gives out the corresponding example.