Course for international guest/part time students
- Faculty
- Faculty of Science
- Organization
- TTK Department of Applied Analysis and Computational Mathematics
- Code
- opfcso1u0um17em
- Title
- Operator semigroups (l)
- Usual semester
- Autumn
- Published semester
- 2026/27/1
- ECTS
- 3
- Language
- en
- Learning outcomes
- Knowledge: getting familiar with the modern notions of operator semigroups Ability: to understand and use the modern operator semigroup methods Attitude: the need to deepen the applied mathematical knowledge, to gain new applied mathematical skills, to develop competencies. The aim to apply the mathematical knowledge for a wide range of problems Autonomy and Responsibility: the importance of the precise formulation of mathematical thinking and notions is clear to the students, who are at the same time aware of the applicability and the boundaries of operator semigroup methods.
- Course content
- Basic concepts of operator semigroups. Main examples and constructions. The concept of generator of operator semigroups. Hille-Yosida theorems. Dissipative operators, Lumer-Phillips theorem. Applications to first- and second-order differential operators. Regularity properties of semigroups. Bounded perturbation, Dyson-Phillips series. Outlook towards unbounded perturbations. Asymptotic properties, spectrum of the semigroup and its generator. Spectral mapping theorems. Operator semigroups and Cauchy problems, well-posedness. Examples.
- Assessment method
- exam
- Bibliography
- lecture notes