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Linear semigroups in Banach spaces. (English) Zbl 0619.47034

Semigroups, theory and applications, Vol. 2, Pap. Autumn Course ICTP, Miramare, Trieste/Italy 1984, Pitman Res. Notes Math. Ser. 152, 93-135 (1986).
[For the entire collection see Zbl 0614.00013.]
The purpose of this text, primarily devoted to non-specialists, is to provide within a limited number of pages an inroduction to the semigroup theory in the form commonly used in the modern research on partial differential equations.
The basic theory of \(C^ 0\) semi-groups is presented in the framework of general Banach spaces. Only simple examples are given here since many good applications can be found in the other texts of the same volume.
For advanced readers, the interesting parts are section 7 where a rather clean treatment of analytic semi-group theory is attempted and the second paragraph of section 10, devoted to the differentiability of weak solutions in the extrapolation space of G. Da Prato and P. Grisvard.

MSC:

47D03 Groups and semigroups of linear operators
47B44 Linear accretive operators, dissipative operators, etc.
35A20 Analyticity in context of PDEs
47F05 General theory of partial differential operators

Citations:

Zbl 0614.00013