The first two chapters of the book deal with linear operators in Banach and Hilbert spaces, chapter 3 deals with Sobolev spaces. Chapters 4,5 and 6 give a clean introduction to the semigroups of linear operators and their applications to partial differential equations. The weakly nonlinear and the semilinear parabolic cases are also studied, and applications are given. The book is very readily written and we can recommend it for a graduate course in semigroup theory.
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