For visitors without knowledge of the place a map is available.
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Bernhard Barth | |
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Office hour for students: by appointment Room: 201 IWRMM (20.52) Tel.: +49-721-608-47862 Email: bernhard.barth@kit.edu |
2. OG IWRMM (20.52) |
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| Semester | Titel | Typ |
|---|---|---|
| Summer Semester 2012 | Kontrolltheorie | |
| Seminar: Fourieranalysis | Seminar | |
| Winter Semester 2011/12 | Seminar Mathematical Biology | Seminar |
| Proseminar: Dynamische Systeme | Proseminar | |
| Summer Semester 2011 | Proseminar Analysis: Ergänzungen zur Analysis | Proseminar |
| Winter Semester 2010/11 | Seminar (Analysis): Weißes Rauschen | Seminar |
| Summer Semester 2010 | Seminar (Analysis) | Seminar |
| Winter Semester 2009/10 | Seminar (Analysis) | Seminar |
Former Teaching
| Wintersemester 2010/11 | Seminar | Weißes Rauschen | ||
| Question time | HM I für die Fachrichtung Bauingenieurwesen | |||
| Sommersemester 2010 | Seminar | Der Pfeil der Zeit | ||
| Wintersemester 2009/10 | Seminar | Wellen |
Given Talks
| Date | Location | Title | Event |
| 20.06.2011 | KIT (Karlsruhe) | A Multiplier Theorem for the Bloch Transform | Seminar of the Research Training Group |
| 16.06.2011 | University of Constance | A Multiplier Theorem for the Bloch Transform | Research Seminar |
If you are interested in the presentation material please write me an email.
Research
Update 07.07.2011: After developing a multiplier result for the Bloch transform in a very general setting the task is now to derive a spectral identity for operators which are decomposable with respect to the Bloch transform.
01.09.2009: Since September 2009 I work in the framework of the graduate program "Analysis, Simulation and design of nanotechnological processes" on my dissertation. The subject of my research will be asymptotically stability of standing waves of nonlinear Schrödinger equation. This issue is, in the case of a sloping potential, largely resolved but in the case of a periodic potential, except in the one-dimensional case, little is known.
Since I have recently incorporated my work I find myself still in the familiarization phase. Currently I am concerned with classical works. Among others, these include
- Multichannel nonlinear scattering for nonintegrable equations. Commun. Math. Phys. 133, No.1, 119-146 (1990). ISSN 0010-3616; ISSN 1432-0916
- Multichannel nonlinear scattering for nonintegrable equations. II: The case of anisotropic potentials and data. J. Differ. Equations 98, No.2, 376-390 (1992). ISSN 0022-0396
- Invariant manifolds for a class of dispersive, Hamiltonian, partial differential equations. J. Differ. Equations 141, No.2, 310-326 (1997). ISSN 0022-0396
A recent study by Cuccagna and Visciglia also considers periodic potentials, but only in the case of one dimension.
- Scattering for small energy solutions of NLS with periodic potential in 1D. C. R., Math., Acad. Sci. Paris 347, No. 5-6, 243-247 (2009). ISSN 1631-073X
As the calculation there uses explicit Blochreprensentations, which are known in the one dimensional case, one can not look forward to get same results this way for higher dimensions. This will be the subject of my research.