Diese Seite auf DE

Event

Evolution Equations [SS200156400]

Type
lecture (V)
Term
SS 2020
SWS
4
Language
Englisch
Appointments
27
Links
ILIAS

Lecturers

Organisation

  • KIT-Fakultät für Mathematik

Part of

Literature

* Engel, Nagel: One-Parameter Semigroups for Linear Evolution Equations
* Pazy: Semigroups of Linear Operators and Applications to Partial Differential Equations

* Arendt, Batty, Hieber, Neubrander: Vector-valued Laplace Transforms and Cauchy Problems
* Davies: One-Parameter Semigroups
* Engel, Nagel: A Short Course of Operator Semigroups
* Fattorini: The Cauchy Problem
* Goldstein: Semigroups of Linear Operators and Applications
* Hille, Phillips: Functional Analysis and Semi-groups
* Lunardi: Analytic Semigroups and Optimal Regularity in Parabolic Problems
* Tanabe: Equations of Evolution

Appointments

  • 20.04.2020 09:45 - 11:15 - Room: 20.30 SR 3.061
  • 22.04.2020 08:00 - 09:30 - Room: 20.30 SR 3.068
  • 27.04.2020 09:45 - 11:15 - Room: 20.30 SR 3.061
  • 29.04.2020 08:00 - 09:30 - Room: 20.30 SR 3.068
  • 04.05.2020 09:45 - 11:15 - Room: 20.30 SR 3.061
  • 06.05.2020 08:00 - 09:30 - Room: 20.30 SR 3.068
  • 11.05.2020 09:45 - 11:15 - Room: 20.30 SR 3.061
  • 13.05.2020 08:00 - 09:30 - Room: 20.30 SR 3.068
  • 18.05.2020 09:45 - 11:15 - Room: 20.30 SR 3.061
  • 20.05.2020 08:00 - 09:30 - Room: 20.30 SR 3.068
  • 25.05.2020 09:45 - 11:15 - Room: 20.30 SR 3.061
  • 27.05.2020 08:00 - 09:30 - Room: 20.30 SR 3.068
  • 03.06.2020 08:00 - 09:30 - Room: 20.30 SR 3.068
  • 08.06.2020 09:45 - 11:15 - Room: 20.30 SR 3.061
  • 10.06.2020 08:00 - 09:30 - Room: 20.30 SR 3.068
  • 15.06.2020 09:45 - 11:15 - Room: 20.30 SR 3.061
  • 17.06.2020 08:00 - 09:30 - Room: 20.30 SR 3.068
  • 22.06.2020 09:45 - 11:15 - Room: 20.30 SR 3.061
  • 24.06.2020 08:00 - 09:30 - Room: 20.30 SR 3.068
  • 29.06.2020 09:45 - 11:15 - Room: 20.30 SR 3.061
  • 01.07.2020 08:00 - 09:30 - Room: 20.30 SR 3.068
  • 06.07.2020 09:45 - 11:15 - Room: 20.30 SR 3.061
  • 08.07.2020 08:00 - 09:30 - Room: 20.30 SR 3.068
  • 13.07.2020 09:45 - 11:15 - Room: 20.30 SR 3.061
  • 15.07.2020 08:00 - 09:30 - Room: 20.30 SR 3.068
  • 20.07.2020 09:45 - 11:15 - Room: 20.30 SR 3.061
  • 22.07.2020 08:00 - 09:30 - Room: 20.30 SR 3.068

Note

Evolution equations describe the time evolution of dynamical systems by an ordinary differential equation in a Banach space. We investigate linear and autonomous (time invariant) problems. In this case the solutions are given by a one-parameter semigroup of linear operators. For such operator semigroups there is a quite complete theory, which allows us to study the properties of the underlying dynamical system. This approach essentially relies on functional analytic methods and results.

We treat the basic existence theorems for linear autonomous evolution equations. In this framework, we then investigate qualitative properties of the solutions, such as regularity and the longterm behavior. Perturbation and approximation results are also studied (which have connections to numerical analysis). The developed theory can be applied to the diffusion, the (damped) wave, and the Schrödinger equation.

Knowledge of the lecture Functional Analysis and of the theory of L^p spaces is required. The necessary parts from the lecture Spectral Theory will be recalled (without proofs) ansd discussed, so that this lecture is not a prerequisite.