Degenerate differential equations in Banach spaces. (English) Zbl 0913.34001

Favini, Angelo; Yagi, Atsushi

Pure and Applied Mathematics, Marcel Dekker. 215. New York, NY: Marcel Dekker. xi, 312 p. (1999).

The book deals with the solvability in a strong sense of degenerate differential problems with many applications to partial differential equations. The approach used is to reduce the problem to a multivalued differential equation and then apply semigroup techniques.
Multivalued linear operators are recalled in Chapter I. In Chapter II degenerate equations of hyperbolic type are studied. In Chapter III and IV degenerate equations of parabolic type are studied, both in the autonomous and nonautonomous case. In Chapter V the general case is studied by using some resolvent properties of the operator which is needed to write the abstract version of the differential problem. In the last two chapters, degenerate equations of higher order are discussed and some alternative approaches and examples are given.
The book is reasonably selfcontained and readable. There is a quite extensive list of references on the subject and a very useful abstract at the beginning of each chapter.

Reviewer: S.Totaro (Firenze)

MSC:

34-02	Research exposition (monographs, survey articles) pertaining to ordinary differential equations
35K65	Degenerate parabolic equations
34G20	Nonlinear differential equations in abstract spaces
34G10	Linear differential equations in abstract spaces
35-02	Research exposition (monographs, survey articles) pertaining to partial differential equations
35L80	Degenerate hyperbolic equations

Keywords:

multivalued operators; parabolic equations; hyperbolic equations; degenerate equations of second order; degenerate equations