Global Classical Solutions for Nonlinear Evolution Equations (Chapman and Hall /Crc Monographs and Surveys in Pure and Applied Mathematics)

This text represents the results originally obtained by S. Lainerman, D. Christodoulou, Y. Choquet-Bruhat, T. Nishida and A. Matsumara on the global existence of classical solutions to the Cauchy problem with small initial data for nonlinear evolution equations. This monograph is devoted to the global existence and the lifespan of classical solutions to the Cauchy problem with small initial data for nonlinear heat equations, nonlinear wave equations and nonlinear Schrodinger equations. The topic has been investigated using a variety of methods by many mathematicians such as L. Hormander, F. John, and S. Klainerman. In this book the authors present a simple and direct method by which to obtain in a unified manner all recent results in the field, including those obtained by themselves and their collaborators. The same method can also be used to treat similar problems for various kinds of nonlinear evolution equations. The volume is self-contained, but assumes knowledge of the basic theory of Sobolev spaces and linear evolution equations. The work will be of interest to researchers and graduate students in pure and applied mathematics, mathematical physics and applied sciences