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Workgroup Functional Analysis

Secretariat
Kollegiengebäude Mathematik (20.30)
Room 2.041

Address
Karlsruher Institut für Technologie
Institut für Analysis
Englerstraße 2
76131 Karlsruhe


natascha.katz@kit.edu


Office hours:
Please see German webpage!

Tel.: +49 721 608 43727

Fax.: +49 721 608 67650

Photo of Roland Schnaubelt Prof. Dr. Roland Schnaubelt

Office hour for students: Wednesday, 10:00 - 11:00, and by appointment
Room: 2-047 (Englerstr. 2) Kollegiengebäude Mathematik (20.30)
Tel.: +49 721 608 48955
Fax.: +49 721 608 47650
Email: schnaubelt@kit.edu

Karlsruher Institut für Technologie
Fakultät für Mathematik
Institut für Analysis
Englerstrasse 2
76131 Karlsruhe
Germany





Semester Titel Typ
Winter Semester 2017/18
Seminar
Seminar
Seminar
Summer Semester 2017
Seminar
Seminar
Winter Semester 2016/17
Seminar
Seminar
Seminar
Summer Semester 2016
Seminar
Proseminar
Winter Semester 2015/16
Seminar
Seminar
Seminar


Teaching

Lecture Notes

  1. Analysis I (in German). Lecture in winter semester 2015/16. Downlowad the pdf file.
  2. Analysis II (in German). Lecture in summer semester 2016. Downlowad the pdf file.
  3. Analysis III (in German). Lecture in winter semester 2016/17. Download the pdf file.
  4. Analysis IV (in German). Lecture in summer semester 2017. Download the pdf file.
  5. Functional Analysis. Lecture in winter semester 2009/10. Downlowad the pdf file.
  6. Functional Analysis. Lecture in winter semester 2014/15. Downlowad the pdf file.
  7. Spectral Theory. Lecture in summer semester 2015. Downlowad the pdf file. (Version of 2010.)
  8. Evolution Equations. Lecture in winter semester 2010/11. Downlowad the pdf file.
  9. Asymptotics of Evolution Equations. Lecture in summer semester 2011. Downlowad the pdf file.
  10. Operator Semigroups and Dispersive Equations. Internet Seminar on Evolution Equations. Winter semester 2012/13. Downlowad the pdf file.

The manuscripts are corrected if mistakes are noted. The date of the respective version is indicated on the titlepage.

Internet Seminar 2017/18: Functional Calculus

The internet seminar on evolutione equation has been organized every year since 1997 by several working groups in Germany, Italy, Hungary and the Netherlands. It was founded by the functional analysis group in Tübingen. The participants are advanced master students and Ph.D students. From October to February the participants obtain weekly study material at a website. They are supervised by local coordinators at their university (in Karlsruhe: P.Kunstmann and R. Schnaubelt). From March to June they work in (internationally mixed) small groups on a project and report on it in June at the final workshop. This year's workshop takes place in Wuppertal from 30 June to 6 July.

This year's internet seminar is organised by Markus Haase (Kiel), Balint Farkas (Wuppertal) and Bernhard Haak (Bordeaux). The course treats the theory and applications of functional calculi of (bounded and unbounded) linear operators on Banach spaces. Roughly speaking, a functional calculus is a consistent way of defining operators of the form f(A) for a given operator A and a class of scalar-valued functions f such that relations between the functions f translate into according relations of the operators f(A). The most prominent example of such a calculus is the Borel calculus for a self-adjoint operator on a Hilbert space, but many important functional calculi (which allow to cover operator semigroups, fractional powers like the square root of an operator, the operator logarithm) can be constructed under much weaker assumptions on the operator. These functional calculi are of particular importance for the theory of evolution equations, where quite many problems can be reduced to the question whether an operator of the form f(A) is bounded or not. Often, this question reduces to a vector-valued singular integral, and hence results from harmonic analysis enter the scene.

Basic knowledge in functional analysis and complex analysis is required. If you are interested, please inform me. One can register for the internet seminar at its web page, where further information is given. See also this description of the course. In Karlsruhe we will discuss the weekly material in the lecture (or better: the reading course) Funktionalkalküle.


You can find the history of this series of seminars on the internet seminar web site of our group.


Research

CRC 1173 Wave phenomena: analysis and numerics

In the Collaborative Research Centre 1173 (07/15 - 06/19), I am speaker of the integrated research group and principal investigator of the four projects

Research interests

  • Qualitative properties of evolution equations:
    • Asymptotic properties of solutions to parabolic and hyperbolic (integro-) partial differential equations: stability, convergence, invariant manifolds.
    • Lp-regularity of linear parabolic partial differential equations with unbounded coefficients.
    • Error analysis for numerical schemes of time integration.
    • Recent research topics: Maxwell's equations, nonlinear Schrödinger equation.
  • Stochastic evolution equations.
  • Control theory.
  • Non-autonomous linear evolution equations: asymptotic theory (in particular, exponential dichotomy), existence theory. In this context: evolution semigroups and operator sum method.
  • Spectral and operator theory.
  • Biomathmatics.

Our webpage gives an overview of the research fields and activities of our working group functional analysis.

Recent preprints

  1. J. Eilinghoff and R. Schnaubelt: Error estimates in L^2 of an ADI splitting scheme for the inhomogeneous Maxwell equations. Download the pdf file.
  2. J. Eilinghoff and R. Schnaubelt: Error analysis of an ADI splitting scheme for the inhomogeneous Maxwell equations. Download the pdf file.
  3. P. D'Ancona, S. Nicaise, R. Schnaubelt: Blow-up for nonlinear Maxwell equations. Submitted. Download the pdf file.
  4. M. Hochbruck, T. Pazur, R. Schnaubelt: Error analysis of implicit Runge--Kutta methods for quasilinear hyperbolic evolution equations. To appear in Numer. Math. Download the pdf file.
  5. T. Jahnke, M. Mikl, R. Schnaubelt: Strang splitting for a semilinear Schrödinger equation with damping and forcing. To appear in J. Math. Anal. Appl. Download the pdf file.
  6. L. Maniar, M. Meyries, R. Schnaubelt: Null controllability for parabolic problems with dynamic boundary conditions of reactive-diffusive type. To appear in Evol. Equ. Control Theory. Download the pdf file.
  7. Y. Latushkin, R. Schnaubelt, Xinyao Yang: Stable foliations near a traveling front for reaction diffusion systems. To appear in Discrete Contin. Dyn. Syst. Ser. B. Download the pdf file.

Publications

The preprint versions of all my papers can be found following this link. You can further download my complete list of publications (pdf file) here.

Book

Jan Prüss, Roland Schnaubelt, Rico Zacher: Mathematische Modelle in der Biologie. Deterministische homogene Systeme. Mathematik Kompakt. Birkhäuser, Basel, 2008. (More information.)


Euro-Maghrebian Workshops on Evolution Equations

Since the late 90s the Euro-Maghrebian Workshops on Evolutions Equations have been organized biannually by working groups in Germany, Italy, and France, as well as Morocco, Algeria and Tunisia. This series was started in 1999 by Rainer Nagel and Abdelaziz Rhandi Marrakesh. In these workshops we put a special emphasis on mini courses about recent topics in evolution equations. An overview of these meetings is given on this website.

Co-organised conferences and sessions

  • 10th Euro - Maghrebian Workshop on Evolution Equations in Blaubeuren, 26.-30.9.2016. See website.
  • Summer school on Wave Phenomena: Analysis and Numerics in Karlsruhe, 12.-15.9.2016. See website.
  • 9th Euro - Maghrebian Workshop on Evolution Equations in Marrakech, 22-26 September 2014. See website.
  • Nonlinear Evolution Equations: Analysis and Numerics in the Mathematical Research Institute Oberwolfach, 16-22 March 2014. See: website, program, participants.
  • Operator Semigroups and Dispersive Equations. Workshop of the 16th Internetseminar on Evolution Equations in Blaubeuren, 10-14 June 2013. See website.
  • 8th Euro - Maghrebian Workshop on Evolution Equations in Lecce, 11-15 June 2012. See website.
  • Evolution Equations: Randomness and Asymptotics in Bad Herrenalb, 10-14 October 2011. See website.
  • 7th Workshop on Control of Distributed Parameter Systems in Wuppertal, 18-22 July 2011. See website.
  • International Conference on Evolution Equations in Schmitten, Germany, 11-15 October 2010. See website.
  • Special session Stability of Partial Differential Equations and Evolution Equations of the 8th AIMS Conference on Dynamical Systems, Differential Equations and Applications in Dresden, Germany, 25-28 July 2010. See website.
  • Workshop Semigroups Everywhere in Tübingen, Germany, 20-22 November 2008.
  • Special Session Operator Semigroups and Evolution Equations of the Joint International Meeting UMI - DMV in Perugia, Italy, 18-22 June 2007.

Projects

  • Principal investigator of the Collaborative Research Centre 1173 Wave phenomena: analysis and numerics (07/15 - 06/19), funded by DFG (Germany).
  • Principal investigator of the Research Training Group 1294 Analysis, Simulation and Design of Nanotechnological Processes (10/10 - 03/15), funded by DFG (Germany).
  • Project Qualitative behavior of parabolic problems with nonlinear dynamical and static boundary conditions (04/09 - 03/11), funded by DFG (Germany).
  • Co-organisor of the cooperation project Functional analytic methods for evolution equations (05/07 - 04/09; 01/11 - 12/12) with L. Maniar and A. Rhandi, Universite de Marrakech, funded by DFG (Germany) and CNRST (Morocco). (Previous related projects: 04/01 - 03/03; 06/04 - 05/06.)
  • Co-organisor of the Marie Curie exchange program Asymptotics of Operator Semigroups (11/12 - 10/16).
  • Co-organisor of the cooperation project Center manifolds and stability of nonlinear partial differential equations (2004/05) with Y. Latushkin, University of Missouri-Columbia, funded by DAAD (Germany) and NSF (USA).

A short curriculum vitae

1988-94 Study of mathematics, physics and philosophy at the Universities of Stuttgart and Tübingen (Germany). Diploma in mathematics, Tübingen
1996 Ph.D. in mathematics, Tübingen
2000 Habilitation in mathematics, Tübingen
2000-06 Assistant Professor at the University of Halle (C2, since 07/01)
2006 Professor (W3) at the Karlsruhe Institute of Technology (until 2009: University of Karlsruhe)

Here you can view a more complete curriculum vitae (pdf file).