Address:Analysis und Scientific Computing
Vienna University of Technology
Wiedner Hauptstraße 8-10
A-1040 Wien, Austria
Telephone: +43 - 1 - 58801 - 10178
Fax: +43 - 1 - 58801 - 11599
Email: achleitner@aurora.anum.tuwien.ac.at
Advisor: Peter Szmolyan
Co-advisor: Alfred Kluwick
Research: I'm interested in dynamical systems and their application to problems in science and technology.
Together with Peter Szmolyan I work on the dynamics and stability of shock waves.
It is a natural idea to study the stability of shock waves by analyzing the spectrum of the linearization along the wave. The Evans function approach to such problems provides a general geometric framework to study and exploit spectral properties of the linearized problem. Briefly speaking, the Evans function is an analytic function of the spectral parameter whose zeros to the right of the essential spectrum correspond to eigenvalues. A shock wave is spectrally stable, if the spectrum of the related linear operator consists of eigenvalues with negative real part and the eigenvalue zero. The interest in the spectral stability stems from the fact that Zumbrun and collaborators have been able to show that spectral stability of a viscous shock wave implies its nonlinear stability.
In the following stability of general small amplitude shock waves has been proved via the Evans function approach and via energy estimates. In these works the smallness of the amplitude is exploited and hence the methods do not apply to the case of large amplitude shock waves.
The aim of my research is to develop new methods to analyze the spectrum in these cases:
Master thesis:
Spectral stability of small amplitude shock profiles of the Jin-Xin model, advisor: Peter Szmolyan, Vienna 2004
Activities: