Welcome to my webpage!

No office hours on 22 May, 29 May and 12 June.

1. Analysis I (in German). Lecture in winter semester 2007/08. Downlowad the pdf file.
2. Analysis II (in German). Lecture in summer semester 2008. Downlowad the pdf file.
3. Analysis III (in German). Lecture in winter semester 2008/09. Downlowad the pdf file.
4. Funktionentheorie I (in German). Lecture in summer semester 2009. Downlowad the pdf file.
5. Functional Analysis. Lecture in winter semester 2009/10. Downlowad the pdf file.
6. Functional Analysis. Lecture in winter semester 2011/12. Downlowad the pdf file.
7. Spectral Theory. Lecture in summer semester 2010. Downlowad the pdf file.
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. The manuscripts Analysis I-III and Funktionentheorie I do not contain proofs, but illustrations and an index.

The internet seminar on evolution equation has been organized every year since 1997 by working groups in Tübingen, Ulm and Karlsruhe, as well as in Italy, the Netherlands, France and Hungary. The participants are advanced master/diploma 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: R. Schnaubelt). From March to May they work in (internationally mixed) small groups on a project and report on it in June at the final workkshop. This year's workshop takes place in Blaubeuren near Ulm, Germany.

This year the internet seminar is organised by our Karlsruhe Team (D. Hundertmark, L. Machinek, M. Meyries, R. Schnaubelt) and treats evolutions equations of dispersive type. Here we consider in particular linear and semilinear wave and Schrödinger equations. The lecture functional analysis is required. Basic facts about spectral theory and Sobolev spaces will briefly recalled iin the course. More details you can find in this pdf file. If interested, please inform Roland Schnaubelt. One can register for the internet seminar at our web page, where further information is given.

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

• Qualitative properties of evolution equations:
  • Asymptotic properties of solutions to parabolic and hyperbolic (integro-) partial differential equations: stability, exponential dichotomy, invariant manifolds, periodic and almost periodic solutions.
  • Lp-regularity of linear parabolic partial differential equations with unbounded coefficients.
  • Recent research topics: Stefan problem with surface tension, nonlinear Schrödinger equation.
• Stochastic evolution equations.
• Control theory.
• Biomathmatics.
• 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.

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

1. Russell Johnson, Yuri Latushkin, Roland Schnaubelt: Reduction principle and asymptotic phase for center manifolds of parabolic systems with nonlinear boundary conditions. Download the pdf file.
2. Mahmoud Baroun, Birgit Jacob, Lahcen Maniar, Roland Schnaubelt: Semilinear observation systems. Download the pdf file.
3. Martin Meyries, Roland Schnaubelt: Maximal regularity with temporal weights for parabolic problems with inhomogeneous boundary conditions. Download the pdf file.
4. Simona Fornaro, Giorgio Metafune, Diego Pallara, Roland Schnaubelt: One-dimensional degenerate operators in L^p-spaces. Download the pdf file.
5. M. Hochbruck, T. Jahnke, R. Schnaubelt, Convergence of an ADI splitting for Maxwells equations. Download the pdf file.

My previous papers you can find following this link (starting from 2006) or among the Preprints der Fakultät für Mathematik der Universität Karlsruhe and the Reports of the Institute of Mathematics of the University of Halle (2000-06).

Here you can download my complete list of publications (pdf file).

• Member of the Research Training Group 1294 Analysis, Simulation and Design of Nanotechnological Processes (10/10 - 03/15), supported by DFG (Germany).
• Project Qualitative behavior of parabolic problems with nonlinear dynamical and static boundary conditions (04/09 - 03/11), supported 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, supported 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, supported by DAAD (Germany) and NSF (USA).

• Nonlinear Evolution Equations: Analysis and Numerics at the Mathematical Research Institute Oberwolfach, 16-22 March 2014.
• 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.

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