Research

Publications

2009-2010

Hillen, T. and Hinow, P. and Wang, Z.A. (2010). Mathematical analysis of a kinetic model for cell movement in network tissues. Discrete and Continuous Dyn. Syst.–B., 14:1-26.


2008-2009

Hadeler, K.P., Hillen, T.J., Lewis, M.A. (in press). Biological modeling with quiescent phases. In Cantrell, S. Cosner, C., and Ruan, S., eds., Lecture notes in Computer Science. CRC Press.

Khassehkan, H., Eberl, H.J., Hillen, T.J. (2009) A nonlinear master equation for a degenerate diffusion model of biofilm growth. In Allen, G., Lecture Notes in Computer Science / Theoretical Computer Sci # 5544: Computational Science, pp 735-744. Springer Berlin / Heidelberg.


2007-2008

Hillen, T. & Painter, K.J. (July 2008). A User's Guide to PDE Models for Chemotaxis. Journal of Mathematical Biology: 35 pages.

Wang, Z., Hillen, T. & Li, M. Mesenchymal Motion Models in One Dimension (accepted for publication May 2008). SIAM Journal on Applied Mathematics: 29 pages. In press.

Wang, Z. & Hillen, T. (September 2007). Pattern Formation for a Chemotaxis Model with Volume Filling Effects. Chaos, 17: 13 pages.


2006-2007

A. Chauviere,  T. Hillen, L. Preziosi. “Modeling the motion of a cell population in the extracellular matrix.” Discrete and Continuous Dynamical Systems, Series B. (2007).

A. Chauviere, T. Hillen, L. Preziosi. “Modeling cell movement in anisotropic and heterogeneous network tissues.” Networks and Heterogeneous Media, (2007): 2: 333-357.

T. Hillen. “M5, Mesoscopic and Macroscopic Models for Mesenchymal Motion.” Journal of Mathematical Biology, (2006): 53: 585-616.

T. Hillen, K. Painter, C. Schmeiser. “Global Existence for Chemotaxis with Finite Sampling Radius.”  Discrete and Continuous Dynamical Systems B, (2007): 7: 125-144.

Z. Wang, T. Hillen. “Shock formation in a chemotaxis model.” Mathematical Methods in the Applied Sciences. (2007) Published Online: 29 May 2007 DOI: 10.1002/mma.898.

 

Affiliated Researchers

  K. Painter, Heriot-Watt U, Edinburgh
Z. Wang, Minnesota;
A. Chauvier, Dresden;
Luigi Preziosi, Torino;
Christian Schmeiser, Vienna;
Peter Hinow, Minnesota;
Katarina Wolf, Wuerzburg
Juan Carlos Chimal, Mexico