ABSTRACT
In this chapter we first present some examples to show how nonlinear evolution equations naturally arise from other branches of science. We will also give definitions of local and global solutions, and outline the theory of global solution. Since this book is designated for graduate students as well as researchers, some basic materials on partial differential equations and Sobolev’s spaces, which will be needed in the remainder of the book, are introduced for convenience. Most results are just recalled without proofs, but the relevant references are given. In the final section of this chapter, some references for further reading are also given.
