Miklavčič, Milan Applied functional analysis and partial differential equations. (English) Zbl 0913.35002 Singapore: World Scientific. x, 294 p. (1998). 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. Reviewer: Marco Biroli (Monza) Cited in 30 Documents MSC: 35-02 Research exposition (monographs, survey articles) pertaining to partial differential equations 47D06 One-parameter semigroups and linear evolution equations 46E35 Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems 35K55 Nonlinear parabolic equations Keywords:weakly nonlinear and the semilinear parabolic cases; graduate course in semigroup theory PDFBibTeX XMLCite \textit{M. Miklavčič}, Applied functional analysis and partial differential equations. Singapore: World Scientific (1998; Zbl 0913.35002)