-
1
-
-
0019188958
-
Biased random walk models for chemotaxis and related diffusion approximations
-
W. Alt, Biased random walk models for chemotaxis and related diffusion approximations, J. Math. Biol. 9 (1980) 147-177.
-
(1980)
J. Math. Biol.
, vol.9
, pp. 147-177
-
-
Alt, W.1
-
2
-
-
0001257097
-
A mathematical model for capillary network formation in the absence of endothelial cell proliferation
-
A. R. A. Anderson and M. A. J. Chaplain, A mathematical model for capillary network formation in the absence of endothelial cell proliferation, Appl. Math. Lett. 11 (1997) 109-114.
-
(1997)
Appl. Math. Lett.
, vol.11
, pp. 109-114
-
-
Anderson, A.R.A.1
Chaplain, M.A.J.2
-
3
-
-
2542432804
-
Mathematical topics in the modelling complex multicellular systems and tumor immune cells competition
-
N. Bellomo, A. Bellouquid and M. Delitala, Mathematical topics in the modelling complex multicellular systems and tumor immune cells competition, Math. Mod. Meth. Appl. Sci. 14 (2004) 1683-1733.
-
(2004)
Math. Mod. Meth. Appl. Sci.
, vol.14
, pp. 1683-1733
-
-
Bellomo, N.1
Bellouquid, A.2
Delitala, M.3
-
4
-
-
33750035381
-
From microscopic to macroscopic description of multicellular systems and biological growing tissues
-
to appear
-
N. Bellomo, A. Bellouquid and M. Herrero, From microscopic to macroscopic description of multicellular systems and biological growing tissues, to appear in J. Comp. Appl. Math.
-
J. Comp. Appl. Math.
-
-
Bellomo, N.1
Bellouquid, A.2
Herrero, M.3
-
5
-
-
27644491983
-
Preface to multiscale cancer modelling - A new frontier in applied mathematics
-
N. Bellomo and P. Maini, Preface to multiscale cancer modelling - a new frontier in applied mathematics, Math. Mod. Meth. Appl. Sci. 15 (2005) iii-viii.
-
(2005)
Math. Mod. Meth. Appl. Sci.
, vol.15
-
-
Bellomo, N.1
Maini, P.2
-
6
-
-
0001580322
-
Global solutions to some parabolic-elliptic systems of chemotaxis
-
P. Biler, Global solutions to some parabolic-elliptic systems of chemotaxis, Adv. Math. Sci. Appl. 9 (1999) 347-359.
-
(1999)
Adv. Math. Sci. Appl.
, vol.9
, pp. 347-359
-
-
Biler, P.1
-
7
-
-
25444471803
-
Derivation of macroscopic equations for individual cell-based models: A formal approach
-
M. Bodnar and J. J. M. Velazquez, Derivation of macroscopic equations for individual cell-based models: A formal approach, Math. Meth. Appl. Sci. 28 (2005) 1757-1779.
-
(2005)
Math. Meth. Appl. Sci.
, vol.28
, pp. 1757-1779
-
-
Bodnar, M.1
Velazquez, J.J.M.2
-
8
-
-
3042580676
-
Kinetic models for chemotaxis and their drift-diffusion limits
-
F. A. C. C. Chalub, P. M. B. Perthame and C. Schmeiser, Kinetic models for chemotaxis and their drift-diffusion limits, Monatsh. Math. 142 (2004) 123-141.
-
(2004)
Monatsh. Math.
, vol.142
, pp. 123-141
-
-
Chalub, F.A.C.C.1
Perthame, P.M.B.2
Schmeiser, C.3
-
10
-
-
29244475370
-
Global convergence of a kinetic model for chemotaxis to a perturbed Keller-Segel model
-
F. A. C. C. Chalub and K. Kang, Global convergence of a kinetic model for chemotaxis to a perturbed Keller-Segel model, Nonlinear Anal. 64 (2006) 686-695.
-
(2006)
Nonlinear Anal.
, vol.64
, pp. 686-695
-
-
Chalub, F.A.C.C.1
Kang, K.2
-
11
-
-
26844499863
-
Global solutions of some chemotaxis and angiogenesis systems in higher space dimensions
-
L. Corrias, B. Perthame and H. Zaag, Global solutions of some chemotaxis and angiogenesis systems in higher space dimensions, Milan J. Math. 72 (2004) 1-28.
-
(2004)
Milan J. Math.
, vol.72
, pp. 1-28
-
-
Corrias, L.1
Perthame, B.2
Zaag, H.3
-
12
-
-
0029391714
-
Transport equations and indices for random and biased cell migration based on single cell properties
-
R. B. Dickinson and R. T. Tranquillo, Transport equations and indices for random and biased cell migration based on single cell properties, SIAM J. Appl. Math. 55 (1995) 1419-1454.
-
(1995)
SIAM J. Appl. Math.
, vol.55
, pp. 1419-1454
-
-
Dickinson, R.B.1
Tranquillo, R.T.2
-
13
-
-
0027342528
-
A stochastic model for cell random motility and haptotaxis based on adhesion receptor fluctuations
-
R. B. Dickinson and R. T. Tranquillo, A stochastic model for cell random motility and haptotaxis based on adhesion receptor fluctuations, J. Math. Biol. 31 (1993) 563-600.
-
(1993)
J. Math. Biol.
, vol.31
, pp. 563-600
-
-
Dickinson, R.B.1
Tranquillo, R.T.2
-
14
-
-
28444437421
-
Kinetic models for chemotaxis: Hydrodynamic limits and spatio-temporal mechanisms
-
Y. Dolak and C. Schmeiser, Kinetic models for chemotaxis: Hydrodynamic limits and spatio-temporal mechanisms, J. Math. Biol. 51 (2005) 595-615.
-
(2005)
J. Math. Biol.
, vol.51
, pp. 595-615
-
-
Dolak, Y.1
Schmeiser, C.2
-
15
-
-
33644610345
-
The Keller-Segel model with logistic sensitivity function and small diffusivity
-
Y. Dolak and C. Schmeiser, The Keller-Segel model with logistic sensitivity function and small diffusivity, SIAM J. Appl. Math. 66 (2005) 286-308.
-
(2005)
SIAM J. Appl. Math.
, vol.66
, pp. 286-308
-
-
Dolak, Y.1
Schmeiser, C.2
-
17
-
-
0030781393
-
Multistep navigation and the combinatorial control of leukocyte chemotaxis
-
E. F. Foxman, J. J. Campbell and E. C. Butcher, Multistep navigation and the combinatorial control of leukocyte chemotaxis, J. Cell Biol. 139 (1997) 1349-1360.
-
(1997)
J. Cell Biol.
, vol.139
, pp. 1349-1360
-
-
Foxman, E.F.1
Campbell, J.J.2
Butcher, E.C.3
-
18
-
-
0041319508
-
Human Polymorphonuclear Leukocytes respond to waves of chemoattractant, like Dictyostelium
-
J. Geiger, D. Wessels and D. R. Soil, Human Polymorphonuclear Leukocytes respond to waves of chemoattractant, like Dictyostelium, Cell Motil. Cytoskeleton 56 (2003) 27-44.
-
(2003)
Cell Motil. Cytoskeleton
, vol.56
, pp. 27-44
-
-
Geiger, J.1
Wessels, D.2
Soil, D.R.3
-
19
-
-
0000507343
-
Finite-time aggregation into a single point in a reaction-diffusion system
-
M. A. Herrero, E. Medina and J. J. L. Velázquez, Finite-time aggregation into a single point in a reaction-diffusion system, Nonlinearity 10 (1997) 1739-1754.
-
(1997)
Nonlinearity
, vol.10
, pp. 1739-1754
-
-
Herrero, M.A.1
Medina, E.2
Velázquez, J.J.L.3
-
21
-
-
0034917420
-
The diffusion limit of transport equations derived from velocity jump processes
-
T. Hillen and H. G. Othmer, The diffusion limit of transport equations derived from velocity jump processes, SIAM J. Appl. Math. 61(3) (2000) 751-775.
-
(2000)
SIAM J. Appl. Math.
, vol.61
, Issue.3
, pp. 751-775
-
-
Hillen, T.1
Othmer, H.G.2
-
22
-
-
0001404830
-
Global existence for a parabolic chemotaxis model with prevention of overcrowding
-
T. Hillen and K. Painter, Global existence for a parabolic chemotaxis model with prevention of overcrowding, Adv. in Appl. Math. 26 (2001) 280-301.
-
(2001)
Adv. in Appl. Math.
, vol.26
, pp. 280-301
-
-
Hillen, T.1
Painter, K.2
-
24
-
-
58149209141
-
Cellular pattern formation during Dictyostelium aggregation
-
T. Höfer, J. A. Sherratt and P. K. Maini, Cellular pattern formation during Dictyostelium aggregation, Physica D 85 (1995) 425-444.
-
(1995)
Physica D
, vol.85
, pp. 425-444
-
-
Höfer, T.1
Sherratt, J.A.2
Maini, P.K.3
-
25
-
-
4744373150
-
From 1970 until present: The Keller-Segel model in chemotaxis and its consequences. I
-
D. Horstmann, From 1970 until present: The Keller-Segel model in chemotaxis and its consequences. I, Jahresber. Deutsch. Math.-Verein. 105 (2003) 103-165.
-
(2003)
Jahresber. Deutsch. Math.-Verein.
, vol.105
, pp. 103-165
-
-
Horstmann, D.1
-
26
-
-
18144362472
-
Drift-diffusion limits of kinetic models for chemotaxis: A generalization
-
H. J. Hwang, K. Kang and A. Stevens, Drift-diffusion limits of kinetic models for chemotaxis: A generalization, Discr. Cont. Dyn. Syst. Ser. B 5 (2005) 319-334.
-
(2005)
Discr. Cont. Dyn. Syst. Ser. B
, vol.5
, pp. 319-334
-
-
Hwang, H.J.1
Kang, K.2
Stevens, A.3
-
27
-
-
22544440302
-
Global solutions of nonlinear transport equations for chemosensitive movement
-
H. J. Hwang, K. Kang and A. Stevens, Global solutions of nonlinear transport equations for chemosensitive movement, SIAM J. Appl. Math. 36 (2005) 1177-1199.
-
(2005)
SIAM J. Appl. Math.
, vol.36
, pp. 1177-1199
-
-
Hwang, H.J.1
Kang, K.2
Stevens, A.3
-
28
-
-
6044249273
-
Stochastic models for cell motion and taxis
-
E. Ionides, K. Fang, R. Isseroff and G. F. Oster, Stochastic models for cell motion and taxis, J. Math. Biol. 48 (2004) 23-37.
-
(2004)
J. Math. Biol.
, vol.48
, pp. 23-37
-
-
Ionides, E.1
Fang, K.2
Isseroff, R.3
Oster, G.F.4
-
29
-
-
0014748565
-
Initiation of slime mold aggregation viewed as an instability
-
E. Keller and L. A. Segel, Initiation of slime mold aggregation viewed as an instability, J. Theor. Biol. 26 (1970) 399-415.
-
(1970)
J. Theor. Biol.
, vol.26
, pp. 399-415
-
-
Keller, E.1
Segel, L.A.2
-
30
-
-
27644503155
-
Micro and meso scales of description corresponding to a model of tissue invasion by solid tumors
-
M. Lachowicz, Micro and meso scales of description corresponding to a model of tissue invasion by solid tumors, Math. Mod. Meth. Appl. Sci. 15 (2005).
-
(2005)
Math. Mod. Meth. Appl. Sci.
, vol.15
-
-
Lachowicz, M.1
-
32
-
-
13844298300
-
An interacting particle system modelling aggregation behavior: From individuals to populations
-
D. Morale, V. Capasso and K. Oelschläger, An interacting particle system modelling aggregation behavior: From individuals to populations, J. Math. Biol. 50 (2005) 49-66.
-
(2005)
J. Math. Biol.
, vol.50
, pp. 49-66
-
-
Morale, D.1
Capasso, V.2
Oelschläger, K.3
-
33
-
-
0042727055
-
Global existence of solutions to a parabolic system for chemotaxis in two space dimensions
-
Athens
-
T. Nagai, Global existence of solutions to a parabolic system for chemotaxis in two space dimensions, in Proc. Second World Congress of Nonlinear Analysts, Part 8 (Athens, 1996), Vol. 30 (1997) 5381-5388.
-
(1996)
Proc. Second World Congress of Nonlinear Analysts, Part 8
, vol.30
, pp. 5381-5388
-
-
Nagai, T.1
-
34
-
-
0010786688
-
Blowup of nonradial solutions to parabolic-elliptic systems modeling chemotaxis in two-dimensional domains
-
T. Nagai, Blowup of nonradial solutions to parabolic-elliptic systems modeling chemotaxis in two-dimensional domains, J. Inequal. Appl. 6 (2001) 37-55.
-
(2001)
J. Inequal. Appl.
, vol.6
, pp. 37-55
-
-
Nagai, T.1
-
35
-
-
0023746235
-
Models of dispersal in biological systems
-
H. G. Othmer, S. R. Dunbar and W. Alt, Models of dispersal in biological systems, J. Math. Biol. 26 (1988) 263-298.
-
(1988)
J. Math. Biol.
, vol.26
, pp. 263-298
-
-
Othmer, H.G.1
Dunbar, S.R.2
Alt, W.3
-
36
-
-
0036553052
-
The diffusion limit of transport equations II: Chemotaxis equations
-
H. G. Othmer and T. Hillen, The Diffusion Limit of Transport Equations II: Chemotaxis Equations, SIAM J. Appl. Math. 62 (2002) 1222-1250.
-
(2002)
SIAM J. Appl. Math.
, vol.62
, pp. 1222-1250
-
-
Othmer, H.G.1
Hillen, T.2
-
37
-
-
0000711026
-
Oscillatory cAMP signaling in the development of dictyostelium discoideum
-
H. G. Othmer and P. Schaap, Oscillatory cAMP Signaling in the Development of Dictyostelium discoideum, Comm. Theor. Biol. 5 (1998) 175-282.
-
(1998)
Comm. Theor. Biol.
, vol.5
, pp. 175-282
-
-
Othmer, H.G.1
Schaap, P.2
-
38
-
-
4944248574
-
Volume-filling and quorum sensing in models for chemosensitive movement
-
K. Painter and T. Hillen, Volume-filling and quorum sensing in models for chemosensitive movement, Canad. Appl. Math. Quart. 10 (2003) 280-301.
-
(2003)
Canad. Appl. Math. Quart.
, vol.10
, pp. 280-301
-
-
Painter, K.1
Hillen, T.2
-
39
-
-
51249193541
-
Random walk with persistence and external bias
-
C. S. Patlak, Random walk with persistence and external bias, Bull. Math. Biophys. 15 (1953) 311-338.
-
(1953)
Bull. Math. Biophys.
, vol.15
, pp. 311-338
-
-
Patlak, C.S.1
-
40
-
-
84867975891
-
PDE models for chemotactic movements: Parabolic, hyperbolic and kinetic
-
B. Perthame, PDE models for chemotactic movements: Parabolic, hyperbolic and kinetic, Appl. Math. 49 (2004) 539-564.
-
(2004)
Appl. Math.
, vol.49
, pp. 539-564
-
-
Perthame, B.1
-
41
-
-
0030407429
-
Biological inferences from a mathematical model for malignant invasion
-
A. J. Perumpanani, J. A. Sherratt, J. Norbury and H. M. Byrne, Biological inferences from a mathematical model for malignant invasion, Invasion Metastasis 16 (1996) 209-221.
-
(1996)
Invasion Metastasis
, vol.16
, pp. 209-221
-
-
Perumpanani, A.J.1
Sherratt, J.A.2
Norbury, J.3
Byrne, H.M.4
-
42
-
-
0032559009
-
Extracellular matrix mediated chemotaxis can impede cell migration
-
A. J. Perumpanani, D. L. Simmons, A. J. H. Gearing, K. M. Miller, G. Ward, J. Norbury, M. Schneemannd and J. A. Sherratt, Extracellular matrix mediated chemotaxis can impede cell migration, Proc. R. Soc. Lond. B 265 (1998) 2347-2352.
-
(1998)
Proc. R. Soc. Lond. B
, vol.265
, pp. 2347-2352
-
-
Perumpanani, A.J.1
Simmons, D.L.2
Gearing, A.J.H.3
Miller, K.M.4
Ward, G.5
Norbury, J.6
Schneemannd, M.7
Sherratt, J.A.8
-
44
-
-
31044443732
-
Multistep navigation of leukocytes: A stochastic model with memory effects
-
D. Ölz, C. Schmeiser and A. Soreff, Multistep navigation of leukocytes: A stochastic model with memory effects, Math. Med. Biol 22 (2005) 291-303.
-
(2005)
Math. Med. Biol
, vol.22
, pp. 291-303
-
-
Ölz, D.1
Schmeiser, C.2
Soreff, A.3
-
46
-
-
0034304765
-
Development and applications of a model for cellular response to multiple chemotactic cues
-
K. Painter, P. K. Maini and H. G. Othmer, Development and applications of a model for cellular response to multiple chemotactic cues, J. Math. Biol. 41 (2000) 285-314.
-
(2000)
J. Math. Biol.
, vol.41
, pp. 285-314
-
-
Painter, K.1
Maini, P.K.2
Othmer, H.G.3
-
47
-
-
21244493212
-
Metastability in chemotaxis models
-
A. B. Potapov and T. Hillen, Metastability in chemotaxis models, J. Dyn. Diff. Eqn. 17 (2005) 293-330.
-
(2005)
J. Dyn. Diff. Eqn.
, vol.17
, pp. 293-330
-
-
Potapov, A.B.1
Hillen, T.2
-
48
-
-
84983941745
-
Runaway phenomena and fluid approximation under high fields in semiconductor kinetic theory
-
F. Poupaud, Runaway phenomena and fluid approximation under high fields in semiconductor kinetic theory, ZAMM Z. Angew. Math. Mech. 72 (1992) 359-372.
-
(1992)
ZAMM Z. Angew. Math. Mech.
, vol.72
, pp. 359-372
-
-
Poupaud, F.1
-
49
-
-
0036708448
-
Establishing direction during chemotaxis in eukaryotic cells
-
W. J. Rappel, P. J. Thomas, H. Levine and W. F. Loomis, Establishing direction during chemotaxis in eukaryotic cells, Biophys. J. 83 (2002) 1361-1367.
-
(2002)
Biophys. J.
, vol.83
, pp. 1361-1367
-
-
Rappel, W.J.1
Thomas, P.J.2
Levine, H.3
Loomis, W.F.4
-
50
-
-
0034455986
-
The derivation of chemotaxis equations as limit dynamics of moderately interacting stochastic many-particle systems
-
A. Stevens, The derivation of chemotaxis equations as limit dynamics of moderately interacting stochastic many-particle systems, SIAM J. Appl. Math. 61 (2004) 183-212.
-
(2004)
SIAM J. Appl. Math.
, vol.61
, pp. 183-212
-
-
Stevens, A.1
-
51
-
-
0000843306
-
Some stochastic processes which arise from a model of the motion of a bacterium
-
D. W. Stroock, Some stochastic processes which arise from a model of the motion of a bacterium, Probab. Th. Rel. Fields 28 (1974) 305-315.
-
(1974)
Probab. Th. Rel. Fields
, vol.28
, pp. 305-315
-
-
Stroock, D.W.1
-
52
-
-
0023079642
-
Stochastic model of leukocyte chemosensory movement
-
R. T. Tranquille and D. A. Lauffenburger, Stochastic model of leukocyte chemosensory movement, J. Math. Biol. 25 (1987) 229-262.
-
(1987)
J. Math. Biol.
, vol.25
, pp. 229-262
-
-
Tranquille, R.T.1
Lauffenburger, D.A.2
-
53
-
-
4544331862
-
Point Dynamics in a singular limit of the Keller-Segel model 1: Motion of the concentration regions
-
J. J. L. Velázquez, Point Dynamics in a singular limit of the Keller-Segel model 1: Motion of the concentration regions, SIAM J. Appl. Math. 64 (2004) 1198-1223.
-
(2004)
SIAM J. Appl. Math.
, vol.64
, pp. 1198-1223
-
-
Velázquez, J.J.L.1
-
54
-
-
0026666635
-
Behaviour of Dictyostelium Amoebae is regulated primarily by the temporal dynamics of the natural cAMP wave
-
D. Wessels, J. Murray and D. R. Soil, Behaviour of Dictyostelium Amoebae is regulated primarily by the temporal dynamics of the natural cAMP wave, Cell Motil. Cytoskeleton 23 (1992) 145-156.
-
(1992)
Cell Motil. Cytoskeleton
, vol.23
, pp. 145-156
-
-
Wessels, D.1
Murray, J.2
Soil, D.R.3
|