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Wissenschaftskolleg (PhD program) Differential Equations
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Publications of WK students                                         > PhD theses

Authors Title Publication status
A. Arnold, C. Sparber Quantum dynamical semigroups for quantum diffusion models with Hartree interaction to appear in Comm. Math. Phys. (2004)
W. Bao, Y. Ge, D. Jaksch, P.A. Markowich, R.M. Weishäupl Convergence rates of dimension reduction on Bose-Einstein condensates Preprint
W. Bao, N.J. Mauser, H.P. Stimming Effective one particle quantum dynamics of electrons: a numerical study of the Schrödinger-Poisson-X-alpha model CMS 1 (2003), pp. 809-828
W. Bao, P. A. Markowich, C. Schmeiser, R.M. Weishäupl On the Gross-Pitaevskii equation with strongly anisotropic confinement: formal asymptotics and numerical experiments Math. Models and Meth. Appl. Sci. 15 (2005), pp. 767-782
N. BenAbdallah, F. Mehats, C. Schmeiser, R.M. Weishäupl The nonlinear Schrödinger equation with a strongly anisotropic harmonic potential SIAM J. Math. Anal. 37 (2005), pp. 189-199
C. Besse, N. Mauser, H.P. Stimming Numerical study of the Davey-Stewartson system M2AN 38 (2004), pp. 1035-1054
H. Brandt, C. Hauert, K. Sigmund Punishment and Reputation in spatial Public Goods Games Proc. R. Soc. Lond. B 270 (2003), pp. 1099-1104
H. Brandt, K. Sigmund The logic of reprobation: assessment and action rules for indirect reciprocation J. Theor. Biol. 231 (2004), pp. 475-486
H. Brandt, K. Sigmund Indirect reciprocity, image-scoring and moral hazard to appear in PNAS
H. Brandt, K. Sigmund, H. Ohtsuki, Y. Iwasa A survey on indirect reciprocity to appear in Y. Takeuchi et al. (eds.), Mathematics for Ecology and Environmental Sciences, Springer
M. Burger, S.-Y. Chu, P. Markowich, C. Schönlieb Instabilities in Cahn-Hilliard and the Willmore Functional Preprint
R. Carles, C. Sparber, P.A. Markowich Semiclassical Asymptotics for Weakly Nonlinear Bloch Waves J. Stat. Phys. 117 (2004), pp. 369-401
J. Carrillo, K. Fellner Long-time asymptotics via entropy methods for diffusion dominated equations preprint no. 2/2004, Univ. Autonoma de Barcelona
F. Chalub, Y. Dolak-Struß, P.A. Markowich, D. Ölz, C. Schmeiser, A. Soreff Model Hierarchies for Cell Aggregation by Chemotaxis Math. Models and Meth. Appl. Sci. 16 (2006), pp. 1173-1198.
L. Desvillettes, K. Fellner Exponential decay towards equilibrium via entropy methods for reaction-diffusion equations preprint, CMLA-ENS de Cachan, 2004
M. Di Francesco, M. Wunsch Large Time Behaviour in Wasserstein Space and Relative Entropy for Bipolar Drift-Diffusion-Poisson Models Preprint
Y. Dolak, T. Hillen Cattaneo Models for Chemosensitive Movement: Numerical Solution and Pattern Formation J. Math. Biol. 46 (2003), pp. 153-170
Y. Dolak, C. Schmeiser A kinetic theory approach to resolving the chemotactic wave paradox in Mathematical Modelling & Computing in Biology and Medicine, (V. Capasso Ed.), ESCULAPIO Pub. Co., Bologna, 2003
Y. Dolak, C. Schmeiser Kinetic models for chemotaxis: Hydrodynamic limits and spatio-temporal mechanisms to appear in J. Math. Biol.
Y. Dolak, C. Schmeiser The Keller-Segel model with small diffusivity to appear in SIAM J. Appl. Math.
J. Dolbeault, P.A. Markowich, D. Ölz, C. Schmeiser Nonlinear Diffusions as Limit of Kinetic Equations with Relaxation Collision Kernels to appear in ARMA
K. Fellner, L. Neumann, C. Schmeiser Convergence to global equilibrium for spatially inhomogeneous kinetic models of non-micro-reversible processes Monatsh. Math. 141 (2004), pp. 289-299
K. Fellner, F. Poupaud, C. Schmeiser Existence and convergence to equilibrium of a kinetic model for cometary flows J. Stat. Phys. 114 (2004), pp. 1481-1499
K. Fellner, C. Schmeiser Burgers-Poisson: a nonlinear dispersive model equation SIAM J. Appl. Math. 64 (2004), pp. 1509-1525
J. Haskovec, C. Schmeiser Transport in semiconductors at saturated velocities Comm. in Math. Sci. 3 (2005), pp. 219-233
Z. Huang, S. Jin, P.A. Markowich, C. Sparber A Bloch Decomposition based Numerical method for Quantum Dynamics in Periodic Potentials Preprint
Z. Huang, S. Jin, P.A. Markowich, C. Sparber, C. Zheng A Time-Splitting Scheme for the Dirac-Maxwell System JCP 208 (2005), pp. 761-789
C. Klein, C. Sparber, P.A. Markowich Numerical Study of Oscillatory Regimes in the Kadomtsev-Petviashvili Equation Preprint
A. Kluwick, N. Viertl Triple-deck regularization of weak hydraulic jumps in a two layer shallow water flow Proc. GAMM meeting 2005
P. A. Markowich, P. Pietra, C. Pohl, H.P. Stimming A Wigner-measure analysis of the Dufort-Frankel scheme for the Schrödinger equation SIAM J. Numer. Anal. 40 (2002), pp. 1281-1310
P. A. Markowich, C. Sparber Highly oscillatory partial differential equations to appear in Proc. ICIAM, Sydney (2003)
L. Neumann, C. Schmeiser Convergence to global equilibrium for a kinetic model for fermions SIAM J. Math. Anal. 36 (2005), pp. 1652-1663
D. Ölz, C. Schmeiser, A. Soreff Multistep navigation of leukocytes: a stochastic model with memory effects to appear in Math. Medicine and Biology
N. Popovic, P. Szmolyan A geometric analysis of the Lagerstrom model problem to appear in JDE
N. Popovic, P. Szmolyan Rigorous asymptotic expansions for Lagerstrom's model equation - a geometric approach to appear in Nonl. Anal. TMA
C. Schönlieb, K.C. Wang Line Segmentation and Analysis With Special Interest to the Duct of a Line Proc. 4th Indian Conf. Comp. Vision, Graphics and Image Processing, Kolkata 2004, pp. 550-555
C. Sparber, R. Carles, P. A. Markowich Semiclassical asymptotics for weakly nonlinear Bloch waves to appear in J. Stat. Phys. (2004)
C. Sparber, J. A. Carrillo, J. Dolbeault, P. A. Markowich On the Long Time Behavior of the Quantum Fokker-Planck Equation Monatsh. Math. 141 (2004), pp. 237-257
C. Sparber, P. A. Markowich Semiclassical asymptotics for the Maxwell-Dirac system J. Math. Phys. 44 (2003), pp. 4555-4572
C. Sparber, N. Mauser, P. A. Markowich Wigner Functions vs. WKB-Techniques in Multivalued Geometrical Optics J. Asympt. Anal. 33 (2003), no. 2, pp. 153-187
R.M. Weishäupl, C. Schmeiser, P.A. Markowich, J.P. Borgna A Hermite Pseudo-spectral method for solving systems of Gross-Pitaevskii equations Preprint

PhD theses

Author Title
Yasmin Dolak Advection dominated models for chemotaxis
Klemens Fellner On two models for charged particle systems: The cometary flow equation and the Burgers-Poisson system
Nina Haiden Cooperation for three or more players
Astrid Huber Singularly perturbed laser equations
Vera Miljanovic On two models for charged particle systems: the cometary flow equation and the Shockley-Read-Hall model
Lukas Neumann Long time properties of solutions to collisional kinetic equations
Nikola Popovic A geometric analysis of the Lagerstrom model: existence of solutions and rigorous asymptotic expansions
Christoph Sparber Rigorous Results in Nonlinear Quantum Dynamics
Hans Peter Stimming (Semi-classical) nonlinear Schrödinger equations: (numerical) analysis and simulations
Rada Weishäupl Dimension Reduction of Weakly Interacting Bose-Einstein Condensates