Welcome to my webpage!
Here you can find the class notes of the lectures I hold more regularly. The manuscripts are corrected if mistakes are noted. The date of the respective version is indicated on the titlepage.
- Analysis 1 (in German). Lecture in winter semester 2020/21. Download the pdf file.
- Analysis 2 (in German). Lecture in summer semester 2021. Download the pdf file.
- Analysis 3 (in German). Lecture in winter semester 2021/22. Download the pdf file.
- Analysis 4 (in German). Lecture in summer semester 2022. Download the pdf file.
- Analysis für das Lehramt (in German). Lecture in summer semester 2019. Download the pdf file.
- Functional Analysis. Lecture in winter semester 2017/18. Download the pdf file. (Version of 2014/15.)
- Spectral Theory. Lecture in summer semester 2015. Download the pdf file.
- Evolution Equations. Lecture in summer semester 2020. Download the pdf file.
- Nonlinear Evolution Equations. Lecture in summer semester 2019. Download the pdf file.
- Nonlinear Maxwell Equations. Lecture in winter semester 2019/20. Download the pdf file.
- Operator Semigroups and Dispersive Equations. Internet Seminar on Evolution Equations. Winter semester 2012/13. Download the pdf file.
Internet Seminar 2022/23: Graphs and Discrete Dirichlet Spaces
The internet seminar on evolution equations 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 16 to 22 July 2023.
This internet seminar is organised by Matthias Keller (Potsdam), Daniel Lenz (Jena), Marcel Schmidt (Leipzig) and Christian Seifert (Hamburg). It treats graphs and operators L defined on them by means of a Dirichlet form. The interplay between the geometric structure of the graph and the spectral theory of L will be studied. Moreover, we investigate the corresponding evolution equation u'(t) + Lu(t) =0. Basic knowledge in functional analysis and complex analysis is needed. One can register for the internet seminar at its web page, where further information is given. See also the description of the course. In Karlsruhe we will discuss the weekly material in the lecture (or better: the reading course) Internetseminar für Evolutionsgleichungen.
You can find the history of this series of seminars on the internet seminar web site of our group.
CRC 1173 Wave phenomena: analysis and numerics
In the second funding period of the Collaborative Research Centre 1173 (07/19 - 06/23), I am speaker of the integrated research group and principal investigator of the projects
- A4: Time integration of Maxwell and wave-type equations (with M. Hochbruck),
- A5: Qualitative behavior of nonlinear Maxwell equations.
- A13: Dispersive estimates for wave equations with low regularity coefficients (with D. Frey, since 01.07.21).
In the first funding period (07/15 - 06/19) I was also a principal investigator of the projects B2: Dispersion Management (with D. Hundertmark) and B5: Biharmonic wave maps (with T. Lamm).
- Qualitative properties of evolution equations, in particular of hyperbolic and parabolic partial differential equations:
- Wellposedness and regularity
- Asymptotic properties of solutions: global existence versus blow-up, stability, convergence, invariant manifolds.
- Error analysis for numerical schemes of time integration.
- Lp-regularity of linear parabolic partial differential equations with unbounded or degenerate coefficients.
- Recent research focus: Maxwell equations.
- Control theory.
- Stochastic evolution equations.
- 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.
Preprints, books, and publications
- R. Schnaubelt: Error analysis of the implicit Euler scheme for the Maxwell-Kerr system. Download the pdf file.
- R. Schippa, R. Schnaubelt: Strichartz estimates for Maxwell equations in media: the structured two dimensional case. Download the pdf file.
- C. Bresch, R. Schnaubelt: Local wellposedness of Maxwell systems with scalar-type retarded material laws. Download the pdf file.
- R. Nutt, R. Schnaubelt: Normal trace inequalities and decay of solutions to the nonlinear Maxwell system with absorbing boundary. Download the pdf file.
- R. Schippa, R. Schnaubelt: Strichartz estimates for Maxwell equations in media: the fully anisotropic case. Download the pdf file.
- V. Müller, R. Schnaubelt, Y. Tomilov: On growth and instability for semilinear evolution equations: an abstract approach.Download the pdf file.
- S. Ohrem, W. Reichel, R. Schnaubelt: Well-posedness for a (1+1)-dimensional wave equation with quasilinear boundary condition. Download the pdf file.
- T. Dohnal, R. Schnaubelt, D. Tietz: Rigorous envelope approximation for interface wave-packets in Maxwell's equations with 2D localization. Download the pdf file.
- J. Prüss, R. Schnaubelt, R. Zacher: Mathematische Modelle in der Biologie. Deterministische homogene Systeme. Mathematik Kompakt. Birkhäuser, Basel, 2008. (More information.)
- W. Dörfler, M. Hochbruck, J. Köhler, A. Rieder, R. Schnaubelt, C. Wieners: Wave Phenomena: Mathematical Analysis and Numerical Approximation. Oberwolfach Seminars 49. Birkhäuser, Cham, 2023. (More information.) Preprint version.
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
- Conference on Mathematics of Wave Phenomena 2022 in Karlsruhe, 14.-18.2.2022. See website.
- Seminar Wave Phenomena: Analysis and Numerics in the Mathematical Research Institute Oberwolfach, 24-30 November 2019. See website.
- Parabolic Evolution Equations, Harmonic Analysis and Spectral Theory in Bad Herrenalb, 6-10 May 2019. See website.
- Conference on Mathematics of Wave Phenomena 2018 in Karlsruhe, 23-27 July 2018. See website.
- 10th Euro - Maghrebian Workshop on Evolution Equations in Blaubeuren, 26-30 September 2016. See website.
- Summer school on Wave Phenomena: Analysis and Numerics in Karlsruhe, 12-15 September 2016. See website.
- 9th Euro - Maghrebian Workshop on Evolution Equations in Marrakech, 22-26 September 2014.
- 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.
- 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.
- Principal investigator of the Collaborative Research Centre 1173 Wave phenomena: analysis and numerics (07/15 - 06/19, 07/19 - 06/23), 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).