WK Differential Equations - Student Member:
Nikola Popovic

Address:
Department of Applied Mathematics and Numerical Analysis
Vienna University of Technology
Wiedner Hauptstraße 8-10
A-1040 Wien, Austria

Telephone: (++43)(1)58801-11530
Fax: (++43)(1)58801-11598
Email: nikola.popovic@tuwien.ac.at

Advisor: Peter Szmolyan

Research: My research so far has focused on the theory of dynamical systems in general and geometric singular perturbation theory respectively invariant manifold techniques and bifurcation theory in particular. The blow-up techniques developed by our group have proven especially useful here. In my master's thesis I took a dynamical systems approach to classical WKB techniques. In my PhD thesis I have been working on the so-called Lagerstrom model, an ODE model problem for low Reynolds number flow. Apart from a geometric proof of existence and uniqueness of solutions, my goal here has been to derive asymptotic solution expansions in the context of geometric singular perturbation theory. In the near future I would like to investigate possible extensions of these geometric techniques to selected PDE problems.

Publications:

1. N. Popovic, Geometric Aspects of WKB Approximation: A Dynamical Systems Approach for the One-Dimensional Stationary Schrödinger Equation, Master's Thesis, Vienna University of Technology, Vienna, Austria, 2000.
   
   
2. N. Popovic, A Geometric Analysis of the Lagerstrom Model: Existence of Solutions and Rigorous Asymptotic Expansions, PhD Thesis, Vienna University of Technology, Vienna, Austria, 2002.
   
   
3. N. Popovic, A Geometric Analysis of the Lagerstrom Model: Existence of Solutions and Rigorous Asymptotic Expansions, to appear in Proceedings of "Equadiff 03", Hasselt, Belgium, 2003.
   
   
4. N. Popovic, P. Szmolyan, A geometric analysis of the Lagerstrom model problem, to appear in JDE.
   
   
5. N. Popovic, P. Szmolyan, Rigorous asymptotic expansions for Lagerstrom's model equation - a geometric approach, submitted to Nonlinear Analysis: Theory, Methods, and Applications.
   
   

Activities:

1. April 2001: Participation in the "Intensive Course Week on Regular and Stochastic Motions in Deterministic Dynamics" at the Limburgs Universitair Centrum in Hasselt, Belgium.
   
   
2. April 2002: Talk given at the "International Workshop on Relaxation Oscillations and Hysteresis" at the University College Cork in Cork, Ireland.
   
   
3. February 2003: Participation in the "International Conference on Applied Mathematics Aplimat 2003" at the Slovak University of Technology in Bratislava, Slovak Republic.
   
   
4. May 2003: Poster presented at the "SIAM Conference on Applicatons of Dynamical Systems" at the Snowbird Ski and Summer Resort in Snowbird, Utah, U.S.A..
   
   
5. July 2003: Talk given at the "International Conference on Differential Equations Equadiff 2003" at the Limburgs Universitair Centrum in Hasselt, Belgium.
   
   
6. September 2003: Talk given at the "International Conference on Applications of Mathematics and Statistics in Economy" at Matej Bel University in Banska Bystrica, Slovak Republic.
   
   
7. September 2003: Talk given at the "Annual Meeting of the German Mathematical Society" at Rostock University in Rostock, Germany.
   
   
8. September 2003: Talk given at the "Annual Meeting of the Austrian Mathematical Society" at the European Academy in Bolzano, Italy.
   
   

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