Transport Equations and their Applications










Bibliography of the CIME Lectures
of Thomas Hillen
(September 2014)

Owl

(Thomas Hillen: www.math.ualberta.ca/~thillen)

The lectures are primarily based on my own papers as listed further below.
There are many more relevant papers from other authors and I like to highlight a few here:
Other references can be found in the papers listed below.

1) Lecture Notes
Modelling with Transport Equations; chemotaxis and anisotropic diffusion
T. Hillen, K.J. Painter, A. Swan.
Draft version, please do not copy or distribute.


pdf-file

2) Relevant Literature from other authors

Keller, E.F.  and Segel, L.A.
Initiation of slime mold aggregation viewed as an instability
J. Theor. Biology
26, 399-415, 1970
Nanjundiah, V.
Chemotaxis, signal relaying and aggregation morphology
J. Theor. Biol.
42, 63-105, 1973
Othmer, H.G. and Dunbar, S.R. and Alt, W.
Models of dispersal in Biological Systems
J. Math. Biol.
26, 263-298, 1988
Othmer, H.G. and Stevens, A.
Aggregation, blow-up and collapse: The ABCs of taxis in reinforced random walks
SIAM J. Appl. Math. 57, 1044-1081, 1997
Horstmann, D.
From 1970 until present: the Keller-Segel model in chemotaxis and its consequences I,
Jahresberichte DMV, 105(3) 103-165, 2003
Painter, K.J.
Modelling migration strategies in the extracellular matrix.
J. Math. Biol.
58:511–543, 2009.










Tree


(Arte al Aperto, Torentino 2014)



3) Relevant papers by Hillen et al.


The lectures are based on my own papers highlighted in BLUE. 
The numbering is the same as on my publication website: publication list.)  
The other papers contain further material on similar topics.

60
K.J. Painter, T. Hillen
Mathematical modelling of glioma growth: the use of Diffusion Tensor Imaging (DTI) data to predict the anisotropic pathways of cancer invasion.
J. Theoretical Biol., 323, 25-39, 2013

preprint
58
T. Hillen, M.A. Lewis,
Mathematical Ecology of Cancer
book chapter in: J.A. Marsan and M. Delitala et al. "Managing complexity, reducing perplexity. Modeling biological systems", Springer 2013

preprint
56
T. Hillen, K.J. Painter, M. Winkler
Anisotropic Diffusion in Oriented Environments can lead to Singularity Formation
European J. Applied Math., 2012. First View online:
DOI: http://dx.doi.org/10.1017/S0956792512000447

preprint
54 T. Hillen, K. Painter
Transport Models for Movement in Oriented Habitats and Anisotropic Diffusion.
In: Dispersal, individual movement and spatial ecology: A mathematical perspective. Eds: M.A. Lewis, P. Maini, S. Petrovskii,  Heidelberg, Springer, 2012, 46 pages




preprint
52 K. Painter, T. Hillen
Spatio-Temporal Chaos in a Chemotaxis Model
Physica D, 240, 363-375, 2011.

Preprint
50 Hillen, T.
Existence Theory for Correlated Random Walks on Bounded Domains
CAMQ, (Canad. Appl. Math. Quart.) 18(1), 1-40, 2010.

  Preprint
44 Hillen, T. and Hinow, P. and Wang, Z.A.
Mathematical Analysis of a  Kinetic Models for Cell Movement in Network Tissues.
Discrete and Continuous Dyn. Syst. - B, 14(3), 1055-1080, 2010

  Preprint
41 Hillen, T. and Painter, K.
A User's Guide to PDE Models for Chemotaxis.
J. Math. Biol., 58(1),   183-217, 2009.
electronic:  http://dx.doi.org/10.1007/s00285-008-0201-3
    Preprint
40

 

Chauviere, A. and Hillen, T. and Preziosi, L.

Modeling cell movement in anisotropic and heterogeneous network tissues

NHM (Networks and Heterogeneous Media), 2, 333-357, 2007.

    Preprint
39

Chauviere, A. and Hillen, T. and Preziosi, L.

Modeling the motion of a cell population in the extracellular matrix

DCDS-B (Discrete and Continuous Dynamical Systems, Series B), Special Issue September  2007, pages 250-259.

   
Preprint
 37
Wang, Zhi An, Hillen, T. and Li, M.
Mesenchymal Motion Models in One Dimension

SIAM J. Appl. Math. 69 (2) 375-397, 2008
  Preprint
36 Wang, Zhi An, and Hillen, T.
Pattern Formation for a Chemotaxis Model with Volume Filling Effects
Chaos, 17(3), 037108 (13 pages), 2007
  Preprint
35 Wang, Zhi An and Hillen, T.
Shock Formation in a Chemotaxis Model
Math. Methods in the Appl. Sciences, 31(1), 45-70, 2008  

Preprint
31
Hillen, Thomas
M^5, Mesoscopic and Macroscopic Models for Mesenchymal Motion
2006,  J. Math. Biol. 53(4), 585-616, 2006.
(electroinc: DOI 10.1007/s00285-006-0017-y)
The original publication is available a www.springerlink.com

Preprint
29 Hillen, Thomas and Painter, Kevin and Schmeiser, Christian
Global Existence for Chemotaxis with Finite Sampling Radius
Discr. Cont. Dyn. Syst. B (DCDS-B), 7(1) 125-144, (2007).

Preprint
25

Hillen, Thomas
On the L^2-Moment Closure of Transport Equations:
The General Case

Discr. Cont. Dyn. Systems, Series B, 5(2) 299-318, 2005

PDF-file
24

Hillen, Thomas
On the L^2-Moment Closure of Transport Equations:
The Cattaneo Approximation

Discr. Cont. Dyn. Systems, Series B, 4(4), 961-982, 2004

PDF-file
23

Hillen, Thomas and Potapov, Alex
The One-Dimensional Chemotaxis Model: Global Existence and Asymptotic Profile
Math. Meth. Appl. Sci., 27:1783-1801, 2004.

   PDF-file
22 Potapov, Alex and Hillen, Thomas
Metastability in Chemotaxis Models
 
J. Dyn. Diff. Eq. , 17(2),   293-330, 2005.. 

PDF-file
21 Painter, Kevin and Hillen, Thomas
Volume-Filling and Quorum Sensing in Models for Chemosensitive Movement
Canadian Applied Mathematics Quarterly, Vol 10(4), 2002, 501-543.

   PDF-file
19 Hillen, Thomas and Levine, Howard
Blow-up in hyperbolic models for chemotaxis.
Zeitschrift fuer Angewandte Mathematik und Physik (ZAMP), vol 54(5), 839-868, 2003.

 PDF-file
18 Hillen, Thomas
Transport Equations with Resting Phases.
European J. Appl. Math. 14(5), 613-636, 2003.

  PDF-file
17 Hillen, Thomas
Hyperbolic Models for Chemosensitive Movement.
Math. Models Methods Appl. Sci., 12(7), 1007-1034, 2002. 
 download 
PDF-file
16 Dolak, Yasmin and Hillen, Thomas
Cattaneo Models for Chemotaxis, Numerical Solution and Pattern Formation.
J. Math. Biol. 46 (2003) 2, 153-170.

 download 
PDF-file
14 Othmer, H.G. and Hillen, Thomas
The Diffusion Limit of Transport Equations II: Chemotaxis Equations.
SIAM J. Appl. Math, 62(4), 1222-1250, 2002.
   download 
PDF-file
13 Hillen, Thomas and Painter, Kevin
Global Existence far a Parabolic Chemotaxis Model  with Prevention of Overcrowding.
Advances in Applied Mathematics, 26(4), 280-301, 2001.
   download 
PDF-file
12 Hillen, Thomas and Rohde, Christian and Lutscher, Frithjof
Existence of weak solutions for a hyperbolic model of chemosensitive movement .
J. Math. Anal. Appl., 260,  173-1999,  2001.
   download 
PDF-file
11 Hillen, Thomas and Othmer, H.G.
The Diffusion Limit of Transport Equations Derived From Velocity Jump Processes.
SIAM J. Appl. Math., 61, 751-775, 2000.
   download 
PDF-file
10 Hillen, Thomas and Stevens, Angela
Hyperbolic models for Chemotaxis in 1-D.
Nonlinear Analysis: Real World Applications 1(3), 409-433, 2000. 
   









Man

(Arte al Aperto, Torentino 2014)





















cone


(Arte al Aperto, Torentino 2014)










































Thomas


(Lago di Caldonazzo, Torentino 2014)