Prof. Dr. Roland Schnaubelt
Karlsruher Institut für Technologie
Fakultät für Mathematik
Institut für Analysis
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. (Version of 2015/16.)
- Analysis 2 (in German). Lecture in summer semester 2021. Download the pdf file. (Version of 2016.)
- Analysis 3 (in German). Lecture in winter semester 2016/17. Download the pdf file.
- Analysis 4 (in German). Lecture in summer semester 2017. 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.
- Operator Semigroups and Dispersive Equations. Internet Seminar on Evolution Equations. Winter semester 2012/13. Download the pdf file.
Internet Seminar 2021/22: Spectral Theory for Operators and Semigroups
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 Salerno from 20 to 25 June 2025.
This internet seminar is organised by Angela Albanese (Lecce), Luca Lorenzi (Parma), Elisabetta Mangino (Lecce) and Abdelaziz Rhandi (Salerno). It first treats spectral theory of operators and then gives an introduction to operator semigroups and lienar evolution equations. Finally, spectral theory is used to study the longterm behavior of solutions. Basic knowledge in functional analysis and complex analysis is needed. It will be possible to register for the internet seminar at its web page, where further information will be given. See also the description of the course. In Karlsruhe we will discuss the weekly material in the lecture (or better: the reading course) Spektraltheorie und Operatorhalbgruppen.
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 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.
Recent preprints, book and publications
- S. Fornaro, G. Metafune, D. Pallara, R. Schnaubelt: Multi-dimensional degenerate operators in L^p-spaces. Submitted. Download the pdf file.
- R. Schippa, R. Schnaubelt: On quasilinear Maxwell equations in two dimensions. Submitted. Download the pdf file.
- R. Schnaubelt, M. Spitz: Local wellposedness of quasilinear Maxwell equations with conservative interface conditions. Submitted. Download the pdf file.
- J. Eilinghoff, R. Schnaubelt: Error estimates in L^2 of an ADI splitting scheme for the inhomogeneous Maxwell equations. Submitted. Download the pdf file.
- P. D'Ancona, R. Schnaubelt: Global Strichartz estimates for an inhomogeneous Maxwell system. Comm. Partial Differential Equations, to appear. Download the pdf file.
- 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
- 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 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. 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.
- 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).