ABSTRACT
The semigroup method is a powerful tool for solving evolution equations. It can be used to deal with many initial value problems or initial boundary value problems for both linear and nonlinear evolution equations, and we will introduce it in this chapter in detail. Sections 2.1-2.4 are mainly concerned with the C0-semigroups of linear contractions, and in Section 2.5 we are devoted to semilinear problems. In order to apply the semigroup method to second-order parabolic equations in the general form, in the sixth section, we briefly introduce the results on the C0-semigroups of bounded operators and analytic semigroups. Some applications are given in Section 2.7. Some references for further reading are given in the last section on bibliographic comments.
