Research Interests

• Qualitative properties of evolution equations, in particular hyperbolic and parabolic partial differential equations:
  • Well-posedness and regularity. Dispersive estimates.
  • Asymptotic properties of solutions: global existence versus blow-up, stability, convergence, invariant manifolds.
  • Error analysis of numerical algorithms for time integration.
  • Lp-regularity of linear parabolic differential equations with unbounded or degenerate coefficients.
  • Current focus: Maxwell system.
• Control theory.
• Spectral and operator theory.

Preprints, books and publications

1. C. Bresch, R. Schnaubelt: Local wellposedness of Maxwell systems with retarded material laws in low regularity. To appear in  NoDEA Nonlinear Differential Equations Appl.   PDF file for download.
2. R. Schnaubelt: Error analysis of the implicit Euler scheme for the Maxwell-Kerr system. PDF-file for download.
3. C. Bresch, R. Schnaubelt: Local wellposedness of Maxwell systems with scalar-type retarded material laws. PDF-file for download.
4. J. Prüss, R. Schnaubelt, R. Zacher: Mathematical models in biology. Deterministic homogeneous systems: Mathematics Compact. Birkhäuser, Basel, 2008. (Further information.)
5. 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.(Further information.)

SFB 1173 Wave phenomena: analysis and numerics

In the three funding periods of the Collaborative Research Center 1173 (07/15 - 06/27) I am spokesperson of the integrated research training group and (co-)applicant of the three subprojects

• 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 co-applicant of the projects B2: Dispersion Management (with D. Hundertmark) and B5: Biharmonic wave maps (with T. Lamm).

Co-organized conferences and sections

• Conference on Mathematics of Wave Phenomena 2025 in Karlsruhe, 24.-28. 2. 2025. See website.
• Conference on Mathematics of Wave Phenomena 2022 in Karlsruhe, 14.-18. 2. 2022. See website.
• Seminar Wave Phenomena: Analysis and Numerics at Mathematisches Forschungsinstitut Oberwolfach, 24-30. 11. 2019. See website.
• Conference Parabolic Evolution Equations, Harmonic Analysis and Spectral Theory in Bad Herrenalb, 6-10. 5. 2019.
• Conference on Mathematics of Wave Phenomena 2018 in Karlsruhe, 23-27. 7. 2018. See website.
• 10th Euro - Maghrebian Workshop on Evolution Equations in Blaubeuren, 26-30. 9. 2016.
• 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. 9. 2014.
• Workshop Nonlinear Evolution Equations: Analysis and Numerics at the Mathematisches Forschungsinstitut Oberwolfach, 16-22. 3. 2014. See website.
• Operator Semigroups and Dispersive Equations. Workshop of the 16th Internetseminar on Evolution Equations in Blaubeuren, 10-14. 6. 2013.
• 8th Euro - Maghrebian Workshop on Evolution Equations in Lecce, 11.-15. 6. 2012. See website.
• Conference Evolution Equations: Randomness and Asymptotics in Bad Herrenalb, 10-14. 10. 2011.
• 7th Workshop on Control of Distributed Parameter Systems in Wuppertal, 18-22.7.2011. See website.
• International Conference on Evolution Equations in Schmitten, 11-15. 10. 2010.
• Section Stability of Partial Differential Equations and Evolution Equations at the 8th AIMS Conference on Dynamical Systems, Differential Equations and Applications in Dresden, 25-28. 7. 2010.
• Workshop Semigroups Everywhere in Tübingen, 20-22. 11. 2008.
• Section Operator Semigroups and Evolution Equations at the Joint International Meeting UMI - DMV in Perugia, Italy, 18-22. 6. 2007.

Euro-Maghrebian Workshops on Evolution Equations

The Euro-Maghrebian Workshops on Evolution Equations have been organized biennially since the late 1990s by several working groups in Germany, Italy, France and Spain, as well as in Morocco, Algeria and Tunisia. They were founded in 1999 by Rainer Nagel and Abdelaziz Rhandi with a conference in Marrakech. A particular focus of these workshops are mini-courses on current topics in evolutionary equations.

Current and past projects

• Co-applicant of the Collaborative Research Center 1173 Wave phenomena: analysis and numerics (07/15 - 06/19, 07/19 - 06/23) funded by the DFG.
• Co-applicant of the Research Training Group Analysis, Simulation and Design of Nanotechnological Processes (10/10 - 03/15), funded by the DFG.
• Project Qualitative behavior of parabolic problems with nonlinear dynamic and static boundary conditions (04/09 - 03/11), funded by the DFG by a 3/4 staff position and further travel and material resources.
• Co-organizer of the cooperation project Functional Analytical Methods for Evolutionary Equations (05/07 - 04/09; 01/11 - 12/12) with L. Maniar and A. Rhandi, Université de Marrakech, funded by DFG and CNRST (Morocco). (Previous projects: 04/01 - 03/03; 06/04 -05/06.)
• Co-organizer of the Marie Curie exchange program Asymptotics of Operator Semigroups (11/12 - 10/16).
• Co-organizer of the collaborative project Center manifolds and stability of nonlinear partial differential equations (2004/05) with Y. Latushkin, University of Missouri-Columbia, funded by DAAD and NSF.

A brief curriculum vitae

Here you can download a more detailed curriculum vitae (PDF).