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.
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pdf-file
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2) Relevant Literature from other
authors
Keller,
E.F. and Segel, L.A.
Initiation of slime mold aggregation viewed as
an instability
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J. Theor. Biology
26, 399-415, 1970
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Nanjundiah, V.
Chemotaxis, signal relaying and aggregation
morphology
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J. Theor. Biol.
42, 63-105, 1973
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Othmer, H.G. and Dunbar, S.R. and
Alt, W.
Models of dispersal in Biological Systems
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J. Math. Biol.
26, 263-298, 1988
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Othmer, H.G. and Stevens, A.
Aggregation, blow-up and collapse: The ABCs of
taxis in reinforced random walks
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SIAM J. Appl. Math. 57, 1044-1081,
1997
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Horstmann, D.
From 1970 until present: the Keller-Segel
model in chemotaxis and its consequences I,
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Jahresberichte DMV, 105(3) 103-165,
2003
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Painter, K.J.
Modelling migration strategies in the
extracellular matrix.
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J. Math. Biol.
58:511–543, 2009.
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(Arte al Aperto, Torentino 2014)
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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
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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 |
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preprint
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58
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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 |
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preprint
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56
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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
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preprint
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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 |
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preprint
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52 |
K. Painter, T.
Hillen
Spatio-Temporal
Chaos in a Chemotaxis Model
Physica D, 240, 363-375, 2011. |
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Preprint
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50 |
Hillen, T.
Existence Theory for Correlated Random
Walks on Bounded Domains
CAMQ, (Canad. Appl. Math. Quart.) 18(1), 1-40,
2010. |
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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 |
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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
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Preprint |
40
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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.
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Preprint
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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.
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Preprint
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37
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Wang, Zhi An,
Hillen, T. and Li, M.
Mesenchymal Motion Models in One Dimension
SIAM
J. Appl. Math. 69 (2) 375-397, 2008 |
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Preprint
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36 |
Wang, Zhi An, and Hillen, T.
Pattern
Formation for a Chemotaxis Model with Volume
Filling Effects
Chaos, 17(3),
037108 (13 pages), 2007 |
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Preprint
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35 |
Wang, Zhi An and Hillen, T.
Shock Formation in a Chemotaxis Model
Math.
Methods in the Appl. Sciences, 31(1), 45-70,
2008
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Preprint
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31
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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 |
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Preprint
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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). |
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Preprint
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25
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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 |
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PDF-file
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24
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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 |
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PDF-file
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23
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Hillen,
Thomas and Potapov, Alex
The One-Dimensional Chemotaxis Model:
Global Existence and Asymptotic Profile
Math. Meth. Appl. Sci., 27:1783-1801,
2004. |
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PDF-file |
22 |
Potapov,
Alex and Hillen, Thomas
Metastability in Chemotaxis Models
J. Dyn. Diff. Eq. ,
17(2), 293-330, 2005..
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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. |
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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.
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PDF-file |
18 |
Hillen,
Thomas
Transport Equations with Resting Phases.
European J. Appl. Math. 14(5), 613-636, 2003. |
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PDF-file |
17 |
Hillen,
Thomas
Hyperbolic Models for Chemosensitive
Movement.
Math. Models Methods Appl. Sci., 12(7),
1007-1034, 2002. |
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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. |
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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. |
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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. |
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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. |
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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. |
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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. |
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(Arte al Aperto, Torentino 2014)
(Arte al Aperto, Torentino 2014)
(Lago di Caldonazzo, Torentino 2014)
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