SoSe 17: Aufbaumodul: Differentialgleichungen III - Dynamical Systems III
Martin Väth
Comments
The lecture is an introduction into semigroup theory for parabolic PDEs, i.e. in particular an introduction into the theory of analytic semigroups, homepage: http://dynamics.mi.fu-berlin.de/lectures/17SS-Vaeth-PDE3/
Fundamentals of the theory of strongly continuous semigroups are assumed to be known from the previous semester.Also the following topics are assumed to be known from the previous semesters:
- Basics of ODEs and dynamical systems
- Fundemenals of the theory of PDEs
- Extended knowlede in analysis und functional analysis (e.g. Lebesgue and Bochner integral)
The methods for analytic semigroups use complex analysis to define e.g. so-called fractional power space for the generators of semigroups. Using these spaces, many problems can be avoided which occur in the theory of strongly continuous semigroups.
However, complex analysis is not assumed to be known by the audience: The required concepts will be introduced in a crash course in one of the first lectures.
Depending on the interest of the audience perhaps some topics will be covered less deeply, and the remaining time might be used to cover other topics from dynamical systems or PDEs. Such possible topics include the theory and application of compact or Fredholm operators or topological methods (in particular degree theory) and their application to dynamical systems and PDEs.
closeSuggested reading
- A. Pazy: Semigroups of linear operators and applications to partial differential equations, Springer, New York, Berlin, Heidelberg, 1992
- D. Henry: Geometric theory of semilinear parabolic equations, Lect. Notes Math. 840, Springer, Berlin, New York, 1981
- H. Amann: Linear and quasilinear parabolic problems I Birkhäuser, Basel, Boston, Berlin, 1995
- A. Lunardi: Analytic semigoups and optimal regularity in parabolic problems Birkhäuser, Basel, Boston, Berlin, 1994
12 Class schedule
Additional appointments
Tue, 2017-05-16 12:00 - 14:00 Tue, 2017-06-06 12:00 - 14:00Regular appointments
Mon, 2017-04-24 14:00 - 16:00