Introduction to semilinear evolution problems. (Introduction aux problèmes d’évolution semi-linéaires.) (French) Zbl 0786.35070

Cazenave, Thierry; Haraux, Alain

Mathématiques & Applications (Paris). 1. Paris: Ellipses, 142 p. (1990).

This book is devoted to present both the abstract theory of linear contraction semigroups in Banach spaces and the applications to a few semilinear evolution equations. Although being a general introduction to the theory of evolution problems, the book contains a few recent results on semilinear problems (heat, wave and Schrödinger equations). The focus of a chapter is the study of the asymptotic behaviour of the solutions with respect to time or the possible blow-up phenomena in a finite time.

Reviewer: D.Blanchard (Mont-Saint-Aignan)

MSC:

35G10	Initial value problems for linear higher-order PDEs
35K25	Higher-order parabolic equations
35B40	Asymptotic behavior of solutions to PDEs
47H20	Semigroups of nonlinear operators
35-02	Research exposition (monographs, survey articles) pertaining to partial differential equations
47-02	Research exposition (monographs, survey articles) pertaining to operator theory

Keywords:

abstract theory of linear contraction semigroups in Banach spaces; applications; semilinear evolution equations; asymptotic behaviour; blow- up phenomena