-
2
-
-
0002042431
-
On convex Sobolev inequalities and the rate of convergence to equilibrium for Fokker-Planck type equations
-
Arnold A, Markowich P, Toscani G and Unterreiter A 2001 On convex Sobolev inequalities and the rate of convergence to equilibrium for Fokker-Planck type equations Commun. Partial Diff. Eqns 26 43-100
-
(2001)
Commun. Partial Diff. Eqns
, vol.26
, Issue.1-2
, pp. 43-100
-
-
Arnold, A.1
Markowich, P.2
Toscani, G.3
Unterreiter, A.4
-
3
-
-
34248370060
-
The Keller-Segel model for chemotaxis with prevention of overcrowding: Linear versus nonlinear diffusion
-
Burger M, Di Francesco M and Dolak-Struß Y 2006 The Keller-Segel model for chemotaxis with prevention of overcrowding: linear versus nonlinear diffusion SIAM J. Math. Anal. 38 1288-315
-
(2006)
SIAM J. Math. Anal.
, vol.38
, Issue.4
, pp. 1288-1315
-
-
Burger, M.1
Di Francesco, M.2
Dolak-Struß, Y.3
-
4
-
-
33645680010
-
Two-dimensional Keller-Segel model: Optimal critical mass and qualitative properties of the solutions
-
Blanchet A, Dolbeault J and Perthame B 2006 Two-dimensional Keller-Segel model: optimal critical mass and qualitative properties of the solutions Electron. J. Diff. Eqns 44 1-33
-
(2006)
J. Diff. Eqns
, vol.44
, pp. 1-33
-
-
Blanchet, A.1
Dolbeault, J.2
Perthame, B.3
-
5
-
-
33746377577
-
Volume effects in the Keller-Segel model, energy preventing blow up
-
Calvez V and Carrillo J A 2006 Volume effects in the Keller-Segel model, energy preventing blow up J. Math. Pures Appl. 86 155-75
-
(2006)
J. Math. Pures Appl.
, vol.86
, Issue.2
, pp. 155-175
-
-
Calvez, V.1
Carrillo, J.A.2
-
6
-
-
49349098770
-
The parabolic Keller-Segel model in
-
Calvez V and Corrias L 2008 The parabolic Keller-Segel model in Commun. Sci. Math. 6 417-47
-
(2008)
Commun. Sci. Math.
, vol.6
, pp. 417-447
-
-
Calvez, V.1
Corrias, L.2
-
7
-
-
43049127974
-
Global existence of solutions to a chemotaxis system with volume filling effect
-
Cieślak T 2008 Global existence of solutions to a chemotaxis system with volume filling effect Colloq. Math. 111 117-34
-
(2008)
Colloq. Math.
, vol.111
, pp. 117-134
-
-
Cieślak, T.1
-
8
-
-
18044401055
-
Entropy dissipation methods for degenerate parabolic problems and generalized Sobolev inequalities
-
Carrillo J A, Jüngel A, Markowich P A, Toscani G and Unterreiter A 2001 Entropy dissipation methods for degenerate parabolic problems and generalized Sobolev inequalities Monatsh. Math. 133 1-82
-
(2001)
Monatsh. Math.
, vol.133
, Issue.1
, pp. 1-82
-
-
Carrillo, J.A.1
Jüngel, A.2
Markowich, P.A.3
Toscani, G.4
Unterreiter, A.5
-
9
-
-
40249114816
-
Asymptotic decay for the solutions of the parabolic-parabolic Keller-Segel chemotaxis system in critical spaces
-
Corrias L and Perthame B 2008 Asymptotic decay for the solutions of the parabolic-parabolic Keller-Segel chemotaxis system in critical spaces Math. Comput. Modelling 47 755-64
-
(2008)
Math. Comput. Modelling
, vol.47
, Issue.7-8
, pp. 755-764
-
-
Corrias, L.1
Perthame, B.2
-
10
-
-
26844499863
-
Global solutions of some chemotaxis and angiogenesis systems in high space dimensions
-
Corrias L, Perthame B and Zaag H 2004 Global solutions of some chemotaxis and angiogenesis systems in high space dimensions Milan J. Math. 72 1-28
-
(2004)
Milan J. Math.
, vol.72
, Issue.1
, pp. 1-28
-
-
Corrias, L.1
Perthame, B.2
Zaag, H.3
-
11
-
-
43049112453
-
Finite-time blow-up in a quasilinear system of chemotaxis
-
Cieślak T and Winkler M 2008 Finite-time blow-up in a quasilinear system of chemotaxis Nonlinearity 21 1057-76
-
(2008)
Nonlinearity
, vol.21
, Issue.5
, pp. 1057-1076
-
-
Cieślak, T.1
Winkler, M.2
-
12
-
-
18644382851
-
Optimal critical mass in the two-dimensional Keller-Segel model in
-
Dolbeault J and Perthame B 2004 Optimal critical mass in the two-dimensional Keller-Segel model in C. R. Math. Acad. Sci. Paris 339 611-6
-
(2004)
C. R. Math. Acad. Sci. Paris
, vol.339
, Issue.9
, pp. 611-616
-
-
Dolbeault, J.1
Perthame, B.2
-
13
-
-
33644610345
-
The Keller-Segel model with logistic sensitivity function and small diffusivity
-
Dolak Y and Schmeiser C 2005 The Keller-Segel model with logistic sensitivity function and small diffusivity SIAM J. Appl. Math. 66 286-308
-
(2005)
SIAM J. Appl. Math.
, vol.66
, Issue.1
, pp. 286-308
-
-
Dolak, Y.1
Schmeiser, C.2
-
14
-
-
4744373150
-
From 1970 until present: The Keller-Segel model in chemotaxis and its consequences: Part i
-
Horstmann D 2003 From 1970 until present: the Keller-Segel model in chemotaxis and its consequences: Part I Jahresbericht der DMV 105 103-65
-
(2003)
Jahresbericht der DMV
, vol.105
, pp. 103-165
-
-
Horstmann, D.1
-
15
-
-
13844288282
-
From 1970 until present: The Keller-Segel model in chemotaxis and its consequences: Part II
-
Horstmann D 2004 From 1970 until present: The Keller-Segel model in chemotaxis and its consequences: Part II Jahresbericht der DMV 106 51-69
-
(2004)
Jahresbericht der DMV
, vol.106
, pp. 51-69
-
-
Horstmann, D.1
-
16
-
-
0001404830
-
Global existence for a parabolic chemotaxis model with prevention of overcrowding
-
Hillen T and Painter K 2001 Global existence for a parabolic chemotaxis model with prevention of overcrowding Adv. Appl. Math. 26 280-301
-
(2001)
Adv. Appl. Math.
, vol.26
, Issue.4
, pp. 280-301
-
-
Hillen, T.1
Painter, K.2
-
18
-
-
0039712703
-
Singularity patterns in a chemotaxis model
-
Herrero M A and Velázquez J J L 1996 Singularity patterns in a chemotaxis model Math. Ann. 306 583-623
-
(1996)
Math. Ann.
, vol.306
, Issue.1
, pp. 583-623
-
-
Herrero, M.A.1
Velázquez, J.J.L.2
-
19
-
-
18144371222
-
Boundedness versus blow-up in a chemotaxis system
-
Horstmann D and Winkler M 2005 Boundedness versus blow-up in a chemotaxis system J. Diff. Eqns 215 52-107
-
(2005)
J. Diff. Eqns
, vol.215
, Issue.1
, pp. 52-107
-
-
Horstmann, D.1
Winkler, M.2
-
20
-
-
84966208077
-
On explosions of solutions to a system of partial differential equations modelling chemotaxis
-
Jäger W and Luckhaus S 1992 On explosions of solutions to a system of partial differential equations modelling chemotaxis Trans. Am. Math. Soc. 329 819-24
-
(1992)
Trans. Am. Math. Soc.
, vol.329
, Issue.2
, pp. 819-824
-
-
Jäger, W.1
Luckhaus, S.2
-
21
-
-
15844396394
-
Preventing blow-up in a chemotaxis model
-
Kowalczyk R 2005 Preventing blow-up in a chemotaxis model J. Math. Anal. Appl. 305 566-88
-
(2005)
J. Math. Anal. Appl.
, vol.305
, Issue.2
, pp. 566-588
-
-
Kowalczyk, R.1
-
22
-
-
0014748565
-
Initiation of slime mold aggregation viewed as an instability
-
Keller E F and Segel L A 1970 Initiation of slime mold aggregation viewed as an instability J. Theor. Biol. 26 399-415
-
(1970)
J. Theor. Biol.
, vol.26
, Issue.3
, pp. 399-415
-
-
Keller, E.F.1
Segel, L.A.2
-
23
-
-
0000911252
-
Blow-up of radially symmetric solutions to a chemotaxis system
-
Nagai T 1995 Blow-up of radially symmetric solutions to a chemotaxis system Adv. Math. Sci. Appl. 5 581-601
-
(1995)
Adv. Math. Sci. Appl.
, vol.5
, pp. 581-601
-
-
Nagai, T.1
-
24
-
-
51249193541
-
Random walk with persistence and external bias
-
Patlak C S 1953 Random walk with persistence and external bias Bull. Math. Biophys. 15 311-38
-
(1953)
Bull. Math. Biophys.
, vol.15
, Issue.3
, pp. 311-338
-
-
Patlak, C.S.1
-
25
-
-
84867975891
-
PDE models for chemotactic movements: Parabolic, hyperbolic and kinetic
-
Perthame B 2004 PDE models for chemotactic movements: parabolic, hyperbolic and kinetic Appl. Math. 49 539-64
-
(2004)
Appl. Math.
, vol.49
, Issue.6
, pp. 539-564
-
-
Perthame, B.1
-
26
-
-
4944248574
-
Volume-filling and quorum sensing in models for chemosensitive movement
-
Painter K and Hillen T 2003 Volume-filling and quorum sensing in models for chemosensitive movement Can. Appl. Math. Q. 10 280-301
-
(2003)
Can. Appl. Math. Q.
, vol.10
, pp. 280-301
-
-
Painter, K.1
Hillen, T.2
|