One-parameter semigroups. (English) Zbl 0636.47051

Clément, Ph.; Heijmans, H. J. A. M.; Angenent, S.; van Duijn, C. J.; de Pagter, B.

CWI Monographs, 5. Centrum voor Wiskunde en Informatica. Amsterdam etc.: North-Holland. IX, 312 p.; Dfl. 105.00 (1987).

In this book the authors have dealt with, in considerable detail, the theory of contraction semigroups of operators on Banach and Hilbert spaces, with special emphasis on the nonlinear theory as developed in the recent past. An outline of some linear theory is also provided. The main approach is via resolvent theory of the Euler form and the approximation methods suggested by the proof of the Hille-Yosida generation theorem. The holomorphic subgroups are also discussed. many pages are devoted to the results on positive contraction semigroups (which are related to the transition probabilities in the theory of stochastic processes).
The book contains illustrative examples and exercises. The applications include problems of (i) diffusion in porous media and (ii).

MSC:

47H20	Semigroups of nonlinear operators
47D03	Groups and semigroups of linear operators
47D07	Markov semigroups and applications to diffusion processes
47-02	Research exposition (monographs, survey articles) pertaining to operator theory

Keywords:

contraction semigroups of operators on Banach and Hilbert spaces; resolvent theory of the Euler form; approximation methods; Hille-Yosida generation theorem; holomorphic subgroups; transition probabilities in the theory of stochastic processes; diffusion in porous media