Research Interests

• Nonlinear PDEs: elliptic-parabolic systems, hyperbolic conservation laws, dispersive equations, free boundary problems
• Kinetic transport equations
• Stochastic differential equations
• Asymptotics: macroscopic limits of kinetic equations, boundary layers, long time behaviour, dispersive limits
• Numerics: nonlinear hyperbolic conservation laws, deterministic methods for kinetic equations, cubature on Wiener space
• Applications: cell movement, chemotaxis, semiconductors, plasmas, cosmic rays, radiative transfer, gas discharge

Present Projects

Title	Funded by	My rôle
Mathematical modelling of actin driven cell migration	WWTF	Principal investigator
Wissenschaftlich-Technische Zusammenarbeit (with France and Spain) Long-time asymptotics for evolution equations in chemistry and biology	ÖAD	Participant
Dendritic snow production	Klimafonds	Subcontractor

Past Projects

Title	Funded by	My rôle
PhD-program (Wissenschaftskolleg) Differential Equation Models in Science and Engineering (2001-2010)	FWF	Speaker
How do cells move? Mathematical modelling of cytoskeletal dynamics and cell migration (2005-2009)	WWTF	Principal investigator
Nonlinear Waves in Kinetic and Macroscopic Models (2006-2010)	FWF	Principal investigator
Marie Curie Early Stage Training multi Site Differential Equation with Applications in Science and Engineering (2006-2010)	EU	Participant + training committee member
Cubature on Wiener Space (2004-2007)	FWF	Principal investigator
Nonlinear Waves (2003-2006)	FWF	Principal investigator
IHP-project Hyperbolic and Kinetic Equations (2002-2005)	EU	Participant
Nonlinear Kinetic Modelling in Stellar Physics, Charged Particle Physics, and Mathematical Biology Austrian-French Cooperation, Amadée (2003-2004)	ÖAD	Coordinator
Fellowship, Dr. Han Zhiqing (2001/2002)	ÖAD	Advisor
Fellowship, Dr. Kedar Nath Uprety (2002)	ÖAD	Advisor
Asymptotic Methods in Kinetic Theory TMR-project (1998-2001)	EU	Participant
Mathematical Analysis of Charged Particle Kinetics Special Semester (1998/99)	ESI	Coordinator
Numerical Modelling of Quantum Phenomena and Kinetic Effects in Semiconductors, Austrian-Italian Cooperation (1997-1998)	ÖAD	Principal investigator
Expansion Methods for the Semiconductor Boltzmann Equation (1996-2000)	FWF	Principal investigator
Physical Modelling and Simulation of Oxygen Precipitation in CZ-Silicon (1995-1996)	ÖNB	Principal investigator
Unsteady Flow in Heated Tube Networks Scholarship, Kedar Nath Uprety (1993-1996)	ÖAD	Advisor
Mathematische Methoden zur Simulation von Halbleiterbauelementen (1992-1995)	FWF	Principal investigator
Strömungssimulation mit Klopfmodell (1992-1993)	FWF	Principal investigator

PhD Students

Name	Thesis Title	Graduation	Affiliation
Andreas Unterreiter	The Switching Behaviour of PN-Diodes in the Case of Low Injection	1991	TU Berlin
Alexander Zwirchmayr	Hydrodynamical Limits and Moment Expansions for the Semiconductor Boltzmann Equation	1996	Finanzmarktaufsicht
Kedar Nath Uprety	Unsteady Fluid Flow in Heated Tube Networks	1996	Tribhuvan Univ., Kathmandu
Klemens Fellner	On two models for charged particle systems: The cometary flow equation and the Burgers-Poisson system	2002	Univ. Graz
Yasmin Dolak-Struss	Advection dominated models for chemotaxis	2004	FFG
Lukas Neumann	Long time properties of solutions to collisional kinetic equations	2005	Univ. Innsbruck
Vera Miljanovic	On two models for charged particle systems: the cometary flow equation and the Shockley-Read-Hall model	2005	UN, CTBTO
Alexander Soreff	Pathwise recombining cubature formulas	2007	BA-CA
Dietmar Ölz	Asymptotic nonlinear models in mathematical physics and biology	2007	RICAM
Jan Haskovec	Stochastic particle approximation to the Keller-Segel model and diffusive limit of the cometary flow equation	2008	RICAM
Sabine Hittmeir	Nonlinear waves in kinetic transport and nonlocal diffusion equations	2009	TU Wien
Christoph Winkler			RICAM, Univ. Wien
Stefanie Hirsch			RICAM, Univ. Wien
Angelika Manhart			RICAM, Univ. Wien
Pedro Acevez Sanchez			Univ. Wien