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Research Interests
- Nonlinear PDEs: elliptic-parabolic systems, hyperbolic conservation laws, dispersive equations, free boundary problems
- Kinetic transport equations
- Stochastic processes
- Asymptotics: macroscopic limits of kinetic equations, boundary layers, long time behaviour, dispersive limits
- Numerics: nonlinear hyperbolic conservation laws, deterministic methods for kinetic equations
- Mathematical cell biology: cell motility, cytoskeleton, chemotaxis
Present Projects
Title Funded by My rôle PhD program (Doktoratskolleg)
Signaling Mechanisms in Cellular HomeostasisFWF Faculty member Special Research Area (SFB)
Taming Complexity in Partial Differential SystemsFWF Project part PI PhD program (Doktoratskolleg)
Dissipation and Dispersion in Nonlinear PDEsFWF Faculty member Modeling of Polarization and Motility of Leukocytes in Three-Dimensional Environments WWTF Principal investigator
Past Projects
Title Funded by My rôle Mathematical modelling of actin driven cell migration (2009-2013) WWTF Principal investigator Wissenschaftlich-Technische Zusammenarbeit (with France and Spain)
Long-time asymptotics for evolution equations in chemistry and biology (2011/12)ÖAD Participant Dendritic snow production (2012) Klimafonds Subcontractor 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 memberCubature 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 Univ. Queensland Jan Haskovec Stochastic particle approximation to the Keller-Segel model and diffusive limit of the cometary flow equation 2008 KAUST Sabine Hittmeir Nonlinear waves in kinetic transport and nonlocal diffusion equations 2009 Univ. Wien Christoph Winkler A close look at actin driven movement: from image analysis to simulation 2015 VOEST Alpine Angelika Manhart Cell movement - zooming in and out 2015 NYU Pedro Acevez Sanchez Fractional diffusion limits of kinetic transport equations 2016 Imperial College Stefanie Hirsch ongoing Univ. Wien