Sep 03, 2019
23. Internetseminar "Evolutionary Equations" 2019/20
The 23rd Internet Seminar on Evolution Equations is devoted to the treatment of Evolutionary Equations. These are ordinary or partial differential equations written in the form
(∂tM(∂t)+A)U=F.
Such equations include, in particular, the heat equation, the wave equation, Maxwell's equations, but also mixed type equations.
The theory is based on a Hilbert space approach using the Fourier-Laplace transform. After introducing unbounded operators and the time derivative in this context, we first study ordinary differential equations, including time delays. We then present the abstract solution theory for partial differential equations and apply it to various examples. Further applications we have in mind are differential-algebraic equations, aspects of homogenization and – of course – the relation of the theory to C_0-semigroups.
This recent space-time framework to treat partial differential equations is based on the seminal paper by Picard in 2009 [Math. Methods Appl. Sci. 32 (2009), 1768–1803]. The developed insights have led to new results in control theory, stochastic partial differential equations, homogenisation theory, differential algebraic equations, delay differential equations and also non-linear partial differential equations.
A detailed outline of the course can be downloaded here.
We expect from the participants basic knowledge in functional analysis (bounded operators, uniform boundedness principle, closed graph theorem, Hahn-Banach theorem), foundations of Hilbert spaces as well as foundations in complex analysis of one variable.
The concept of the “Internet Seminar” originates in 1998 when Rainer Nagel (Tübingen) organized the first Internet Seminar. Since then, many schools have been organized in the same spirit and the experience of the previous editions has shown that these schools are much more effective than traditional schools where participants have a much more passive role. The course is organised in three phases.
- In Phase 1 (October-February), a weekly lecture will be freely accessible over the internet via the ISEM website. The aim of the lectures is to present the theoretic background which lies behind current ongoing research.
- In Phase 2 (April - June), the participants will form small international groups to work on diverse projects which supplement the theory of Phase 1 and provide some applications of it.
- Finally, Phase 3 (10 June - 16 June 2019) consists in a final workshop in Wuppertal, where the teams will present their projects and additional lectures will be delivered by leading experts.
ISem team
Christian Seifert (Hamburg), Sascha Trostorff (Kiel), Marcus Waurick (Strathclyde)