Address:Universität Wien
Institut für Mathematik
Nordbergstrasse 15
(Office: C715)
1090 Wien, Austria
Telephone: +43 1 4277 507 15
Fax: +43 1 4277 506 65
Email: Lukas.Neumann@univie.ac.at
Advisor: N. Mauser
Co-Advisor: C. Schmeiser
RESEARCH:
Analysis of partial differential equations arising from mathematical Physics.
I used the entropy entropy-dissipation approach to study the long time behavior of solutions to kinetic equations. In a first step we applied the method to quite general linear collision operators and in a second work we extended the result to a nonlinear operator including the pauli principle for fermions. Recently I study uniform in time regularity for a class of collisional kinetic equations. Establishing such bounds is necessary to give convergence rates for the entropy method. Furthermore I am especially interested in optimal mass transportation and macroscopic limits of particle systems.
PUBLICATIONS:
-
P1. Convergence to global equilibrium for spatially inhomogeneous kinetic models of non micro-reversible processes, to appear in Monatshefte für Mathematik, 2004.
Joint work with K. Fellner and C. Schmeiser: preprint ps.gz.
- P2. Convergence to global equilibrium for a kinetic model for fermions
, to appear in SIAM J. Math. Anal. 2004
Joint work with
C. Schmeiser:
preprint ps.gz.
Fixpunktsätze; Advisor: W. Förg-Rob at the University of Innsbruck, Department for Mathematics.
SCIENTIFIC ACTIVITIES:
- October 2002: Participant in the Oberwolfach - Seminar: "Mass Transport Problems and Applications".
- February 2003: Participant in the first annual meeting of the HYKE-network: A HYKE.
- Mai - August 2003:
Four months HYKE pre-doc employment at the
Unité de Mathématiques Pures et Appliquées,
Ecole Normale Supérieure de Lyon :
Research group of C. Villani.
- April 2004: Participant in the second annual meeting of the HYKE-network: A HYKE 2.
- June 2004: Participation in the Summer School on "Methods and Models of Kinetic Theory" in Porto Ercole.