Welcome to my webpage!

No office hours on 10 and 17 October.

Teaching

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.

1. Analysis 1 (in German). Lecture in winter semester 2020/21. Download the pdf file.
2. Analysis 2 (in German). Lecture in summer semester 2021. Download the pdf file.
3. Analysis 3 (in German). Lecture in winter semester 2021/22. Download the pdf file.
4. Analysis 4 (in German). Lecture in summer semester 2022. Download the pdf file.
5. Analysis für das Lehramt (in German). Lecture in summer semester 2019. Download the pdf file.
6. Functional Analysis. Lecture in winter semester 2017/18. Download the pdf file.
7. Spectral Theory. Lecture in summer semester 2023. Download the pdf file.
8. Evolution Equations. Lecture in summer semester 2020. Download the pdf file.
9. Nonlinear Evolution Equations. Lecture in summer semester 2019. Download the pdf file.
10. Nonlinear Maxwell Equations. Lecture in winter semester 2019/20. Download the pdf file.
11. Operator Semigroups and Dispersive Equations. Internet Seminar on Evolution Equations. Winter semester 2012/13. Download the pdf file.

Internet Seminar 2023/24: Harmonic Analysis Techniques for Elliptic Operators

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: D. Frey, P.Kunstmann, R. Schnaubelt and P. Tolksdorf). From April 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 Luminy near Marseille from 17 to 21 June 2024.
This internet seminar is organised by Moritz Egert (Darmstadt), Robert Haller (Darmstadt), Sylvie Monniaux (Marseille), and Patrick Tolksdorf (Karlsruhe). It presents how properties of elliptic operators in divergence form can be revealed by modern techniques of harmonic analysis. While classical Fourier analysis is well suited to analyze the Laplacian, it turns out that the analysis of general elliptic operators requires some kind of Fourier anaylsis that is adapted to that operator. The developed techniques will finally be used to solve the famous Kato Square Root Problem. Basic knowledge in functional analysis and complex analysis as well as on the Frouier transform are 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.

Research

CRC 1173 Wave phenomena: analysis and numerics

In the three funding periods of the Collaborative Research Centre 1173 (07/15 - 06/27), I have been 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).

Research interests

• Qualitative properties of evolution equations, in particular of hyperbolic and parabolic partial differential equations:
  • Wellposedness and regularity. Dispersive estimates.
  • 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.
• Spectral and operator theory.

Preprints, books, and publications

1. R. Schnaubelt: Error analysis of the implicit Euler scheme for the Maxwell-Kerr system. Download the pdf file.
2. C. Bresch, R. Schnaubelt: Local wellposedness of Maxwell systems with scalar-type retarded material laws. Download the pdf file.
3. R. Nutt, R. Schnaubelt: Normal trace inequalities and decay of solutions to the nonlinear Maxwell system with absorbing boundary. Download the pdf file.
4. S. Ohrem, W. Reichel, R. Schnaubelt: Well-posedness for a (1+1)-dimensional wave equation with quasilinear boundary condition. Download the pdf file.
5. V. Müller, R. Schnaubelt, Y. Tomilov: On growth and instability for semilinear evolution equations: an abstract approach. To appear in Math. Ann. Download the pdf file.
6. R. Schippa, R. Schnaubelt: Strichartz estimates for Maxwell equations in media: the fully anisotropic case. To appear in J. Hyperbolic Differ. Equ. Download the pdf file.]
7. T. Dohnal, R. Schnaubelt, D. Tietz: Rigorous envelope approximation for interface wave-packets in Maxwell's equations with 2D localization. To appear in SIAM J. Math. Anal. Download the pdf file.
8. J. Prüss, R. Schnaubelt, R. Zacher: Mathematische Modelle in der Biologie. Deterministische homogene Systeme. Mathematik Kompakt. Birkhäuser, Basel, 2008. (More information.)
9. 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.)

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.

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.

Projects

• 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

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