# Semigroups and delay equations, spring 2014

# Semigroups and delay equations, spring 2014

### Lecturer

### Scope

10 sp.

### Type

Advanced studies

### Prerequisites

Basic knowledge of ordinary differential equations and linear partial differential equations, elements of functional analysis (including the Hahn-Banach, Banach-Steinhaus and closed graph theorems), elements of measure and integration (including the Riesz representation theorems) and a passion for pure mathematics.

### Content

The basic theory of one-parameter semigroups of linear operators on Banach spaces. Strongly continuous semigroups, adjoint semigroups. The abstract Cauchy problem. Perturbation theory. Spectral Analysis. Applications to nonlinear delay equations. The principle of linearised (in)stability.

The lectures will be based on material that has been published in books and journal articles (see bibliography below).

### Lectures

Weeks 3-9 and 11-18, Tuesday 14-16 in room D123 and Wednesday 14-16 in room C122. Two hours of exercise classes per week.

Easter Holiday 17.-23.4.

### Exams

Final exam.

### Bibliography

**Books**

P.L. Butzer, H. Berens, Semi-Groups of Operators and Approximation, Springer-Verlag, Berlin, Heidelberg, New York, 1967.

Clément, Ph.; Heijmans, H. J. A. M.; Angenent, S.; van Duijn, C. J.; de Pagter, B. One-parameter semigroups. CWI Monographs, 5. North-Holland Publishing Co., Amsterdam, 1987. x+312 pp. ISBN: 0-444-70284-9

O. Diekmann, S.A. van Gils, S.M. Verduyn Lunel, H.-O. Walther, Delay Equations. Functional-, Complex-, and Nonlinear Analysis, Springer-Verlag, New York, 1995.

Engel, Klaus-Jochen; Nagel, Rainer One-parameter semigroups for linear evolution equations. Graduate Texts in Mathematics, 194. Springer-Verlag, New York, 2000. xxii+586 pp. ISBN: 0-387-98463-1

Goldstein, Jerome A. Semigroups of linear operators and applications. Oxford Mathematical Monographs. The Clarendon Press, Oxford University Press, New York, 1985. x+245 pp. ISBN: 0-19-503540-2

A. Pazy, Semigroups of Linear Operators and Applications to Partial Differential Equations, Springer-Verlag, New York, 1983.

**Articles**

### Registration

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### Exercises

### Notice: Time and room has been changed by the request of students

Group | Day | Time | Place | Teacher |
---|---|---|---|---|

1. | Friday | 14-16 | CK107 | Anssi Mirka |