-
1
-
-
79957801928
-
Local and global well-posedness for aggregation equations and Patlak-Keller-Segel models with degenerate diffusion
-
J. Bedrossian, N. Rodríguez, and A. Bertozzi, Local and global well-posedness for aggregation equations and Patlak-Keller-Segel models with degenerate diffusion, Nonlinearity, 24 (2011), pp. 1683-1714.
-
(2011)
Nonlinearity
, vol.24
, pp. 1683-1714
-
-
Bedrossian, J.1
Rodríguez, N.2
Bertozzi, A.3
-
2
-
-
84855936220
-
Functional inequalities, thick tails and asymptotics for the critical mass Patlak-Keller-Segel model
-
A. Blanchet, E. A. Carlen, and J. A. Carrillo, Functional inequalities, thick tails and asymptotics for the critical mass Patlak-Keller-Segel model, J. Funct. Anal., 262 (2012), pp. 2142-2230.
-
(2012)
J. Funct. Anal.
, vol.262
, pp. 2142-2230
-
-
Blanchet, A.1
Carlen, E.A.2
Carrillo, J.A.3
-
3
-
-
60449088258
-
Critical mass for a Patlak-Keller-Segel model with degenerate diffusion in higher dimensions
-
A. Blanchet, J. A. Carrillo, and P. Laurencot, Critical mass for a Patlak-Keller-Segel model with degenerate diffusion in higher dimensions, Calc. Var., 35 (2009), pp. 133-168.
-
(2009)
Calc. Var.
, vol.35
, pp. 133-168
-
-
Blanchet, A.1
Carrillo, J.A.2
Laurencot, P.3
-
4
-
-
52349087894
-
Infinite time aggregation for the critical Patlak-Keller-Segel model in R2
-
A. Blanchet, J. A. Carrillo, and N. Masmoudi, Infinite time aggregation for the critical Patlak-Keller-Segel model in R2, Comm. Pure Appl. Math., 61 (2008), pp. 1449-1481.
-
(2008)
Comm. Pure Appl. Math.
, vol.61
, pp. 1449-1481
-
-
Blanchet, A.1
Carrillo, J.A.2
Masmoudi, N.3
-
6
-
-
84990617031
-
Asymptotic symmetry and local behavior of semilinear elliptic equations with critical Sobolev growth
-
L. A. Caffarelli, B. Gidas, and J. Spruck, Asymptotic symmetry and local behavior of semilinear elliptic equations with critical Sobolev growth, Comm. Pure Appl. Math., 42 (1989), pp. 271-297.
-
(1989)
Comm. Pure Appl. Math.
, vol.42
, pp. 271-297
-
-
Caffarelli, L.A.1
Gidas, B.2
Spruck, J.3
-
7
-
-
84861381595
-
-
V. Calvez, L. Corrias, and M. A. Ebde, Blow-Up, Concentration Phenomenon and Global Existence for the Keller-Segel Model in High Dimension, http://arxiv.org/abs/1003.4182v1, 2010.
-
(2010)
Blow-Up, Concentration Phenomenon and Global Existence for the Keller-Segel Model in High Dimension
-
-
Calvez, V.1
Corrias, L.2
Ebde, M.A.3
-
8
-
-
33746377577
-
Volume effects in the Keller-Segel model: energy estimates preventing blow-up
-
DOI 10.1016/j.matpur.2006.04.002, PII S0021782406000511
-
V. Calvez and J. A. Carrillo, Volume effects in the Keller-Segel model: Energy estimates preventing blow-up, J. Math. Pures Appl., 86 (2006), pp. 155-175. (Pubitemid 44111669)
-
(2006)
Journal des Mathematiques Pures et Appliquees
, vol.86
, Issue.2
, pp. 155-175
-
-
Calvez, V.1
Carrillo, J.A.2
-
9
-
-
69749121629
-
Modified keller-segel system and critical mass for the log interaction kernel, in nonlinear partial differential equations and related analysis
-
AMS, Providence, RI
-
V. Calvez, B. Perthame, and M. Sharifi tabar, Modified Keller-Segel system and critical mass for the log interaction kernel, in Nonlinear Partial Differential Equations and Related Analysis, Contemp. Math. 429, AMS, Providence, RI, 2007, pp. 45-62.
-
(2007)
Contemp. Math.
, vol.429
, pp. 45-62
-
-
Calvez, V.1
Perthame, B.2
Sharifi Tabar, M.3
-
10
-
-
84860678370
-
A note on the subcritical two dimensional Keller-Segel system
-
DOI 10.1007/s10440-011-9660-4
-
J. A. Carrillo, L. Chen, J.-G. Liu, and J. Wang, A note on the subcritical two dimensional Keller-Segel system, Acta Appl. Math., (2011), DOI 10.1007/s10440-011-9660-4.
-
(2011)
Acta Appl. Math.
-
-
Carrillo, J.A.1
Chen, L.2
Liu, J.-G.3
Wang, J.4
-
11
-
-
84974004406
-
Classification of solutions of some nonlinear elliptic equations
-
W. X. Chen and C. M. Li, Classification of solutions of some nonlinear elliptic equations, Duke Math. J., 63 (1991), pp. 615-622.
-
(1991)
Duke Math. J.
, vol.63
, pp. 615-622
-
-
Chen, W.X.1
Li, C.M.2
-
12
-
-
61649113706
-
Finite time blow-up for radially symmetric solutions to a critical quasilinear Smoluchowski-Poisson system
-
T. Cieślak and P. Laurencot, Finite time blow-up for radially symmetric solutions to a critical quasilinear Smoluchowski-Poisson system, C. R. Math. Acad. Sci. Paris, 347 (2009), pp. 237-242.
-
(2009)
C. R. Math. Acad. Sci. Paris
, vol.347
, pp. 237-242
-
-
Cieślak, T.1
Laurencot, P.2
-
13
-
-
43049112453
-
Finite-time blow-up in a quasilinear system of chemotaxis
-
T. Cieślak and M. Winkler, Finite-time blow-up in a quasilinear system of chemotaxis, Nonlinearity, 21 (2008), pp. 1057-1076.
-
(2008)
Nonlinearity
, vol.21
, pp. 1057-1076
-
-
Cieślak, T.1
Winkler, M.2
-
14
-
-
84968509708
-
Existence de nappes de tourbillon en dimension deux
-
J. M. Delort, Existence de nappes de tourbillon en dimension deux, J. Amer. Math. Soc., 4 (1991), pp. 553-386.
-
(1991)
J. Amer. Math. Soc.
, vol.4
, pp. 553-386
-
-
Delort, J.M.1
-
15
-
-
18644382851
-
2
-
DOI 10.1016/j.crma.2004.08.011, PII S1631073X04004388
-
J. Dolbeault and B. Perthame, Optimal critical mass in the two dimensional Keller-Segel model in R2, C. R. Acad. Sci. Paris Ser. I Math., 339 (2004), pp. 611-616. (Pubitemid 41447527)
-
(2004)
Comptes Rendus Mathematique
, vol.339
, Issue.9
, pp. 611-616
-
-
Dolbeault, J.1
Perthame, B.2
-
16
-
-
0001079647
-
On the blowing up of solutions of the Cauchy problem for ut = ?u+u1+a
-
H. Fujita, On the blowing up of solutions of the Cauchy problem for ut = ?u+u1+a, J. Fac. Sci. Univ. Tokyo Sect. I, 13 (1966), pp. 109-124.
-
(1966)
J. Fac. Sci. Univ. Tokyo Sect.
, vol.1
, Issue.13
, pp. 109-124
-
-
Fujita, H.1
-
17
-
-
4944248574
-
Volume filling and quorum sensing in models for chemosensitive movement
-
K. J. Painter and T. Hillen, Volume filling and quorum sensing in models for chemosensitive movement, Can. Appl. Math. Q., 10 (2002), pp. 501-543.
-
(2002)
Can. Appl. Math. Q.
, vol.10
, pp. 501-543
-
-
Painter, K.J.1
Hillen, T.2
-
18
-
-
63049107118
-
A user's guide to PDE models for chemotaxis system
-
T. Hillen and K. J. Painter, A user's guide to PDE models for chemotaxis system, J. Math. Biol., 58 (2009), pp. 183-217.
-
(2009)
J. Math. Biol.
, vol.58
, pp. 183-217
-
-
Hillen, T.1
Painter, K.J.2
-
19
-
-
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), pp. 103-165.
-
(2003)
Jahresber. Deutsch. Math.-Verein.
, vol.105
, pp. 103-165
-
-
Horstmann, D.1
-
20
-
-
18144371222
-
Boundedness vs. blow-up in a chemotaxis system
-
DOI 10.1016/j.jde.2004.10.022, PII S0022039604004152
-
D. Horstmann and M. Winkler, Boundedness vs. blow-up in a chemotaxis system, J. Differential Equations, 215 (2005), pp. 52-107. (Pubitemid 40621900)
-
(2005)
Journal of Differential Equations
, vol.215
, Issue.1
, pp. 52-107
-
-
Horstmann, D.1
Winkler, M.2
-
21
-
-
80655127877
-
Global existence of weak solutions to quasilinear degenerate Keller-Segel systems of parabolic-parabolic type
-
S. Ishida and T. Yokota, Global existence of weak solutions to quasilinear degenerate Keller-Segel systems of parabolic-parabolic type, J. Differential Equations, 252 (2012), pp. 1421-1440.
-
(2012)
J. Differential Equations
, vol.252
, pp. 1421-1440
-
-
Ishida, S.1
Yokota, T.2
-
22
-
-
41149163591
-
Nonlinear instability in gravitational Euler-Poisson systems for ? = 6/5
-
J. Jang, Nonlinear instability in gravitational Euler-Poisson systems for ? = 6/5, Arch. Ration. Mech. Anal., 188 (2008), pp. 265-307.
-
(2008)
Arch. Ration. Mech. Anal.
, vol.188
, pp. 265-307
-
-
Jang, J.1
-
23
-
-
41449086239
-
On the global existence of solutions to an aggregation model
-
R. Kowalczyk and Z. Szymańska, On the global existence of solutions to an aggregation model, J. Math. Anal. Appl., 343 (2008), pp. 379-398.
-
(2008)
J. Math. Anal. Appl.
, vol.343
, pp. 379-398
-
-
Kowalczyk, R.1
Szymańska, Z.2
-
24
-
-
34548405009
-
Extension au cas des trois dimensions de la question du tracé géographique Note VI
-
G. Monge, ed., Bachelier, Paris
-
J. Liouville, Extension au cas des trois dimensions de la question du tracé géographique, Note VI, in Applications de l'Analyse á la Géométrie, G. Monge, ed., Bachelier, Paris, 1850, pp. 609-617.
-
(1850)
Applications de l'Analyse á la Géométrie
, pp. 609-617
-
-
Liouville, J.1
-
25
-
-
0004148844
-
-
2nd ed., Grad. Stud. Math. AMS, Providence, RI
-
E. H. Lieb and M. Loss, Analysis, 2nd ed., Grad. Stud. Math. 14, AMS, Providence, RI, 2001.
-
(2001)
Analysis
, vol.14
-
-
Lieb, E.H.1
Loss, M.2
-
26
-
-
33746275846
-
Large time behavior of solutions in super-critical cases to degenerate Keller-Segel systems
-
DOI 10.1051/m2an:2006025
-
S. Luckhaus and Y. Sugiyama, Large time behavior of solutions in super-critical cases to degenerate Keller-Segel systems, M2AN Math. Model. Numer. Anal., 40 (2006), pp. 597-621. (Pubitemid 44106970)
-
(2006)
Mathematical Modelling and Numerical Analysis
, vol.40
, Issue.3
, pp. 597-621
-
-
Luckhaus, S.1
Sugiyama, Y.2
-
27
-
-
0037144962
-
Self-similar solutions to a parabolic system modeling chemotaxis
-
Y. Naito, T. Suzuki, and K. Yoshida, Self-similar solutions to a parabolic system modeling chemotaxis, J. Differential Equations, 184 (2002), pp. 386-421.
-
(2002)
J. Differential Equations
, vol.184
, pp. 386-421
-
-
Naito, Y.1
Suzuki, T.2
Yoshida, K.3
-
29
-
-
0042766523
-
Non-linear stability of gaseous stars
-
G. Rein, Non-linear stability of gaseous stars, Arch. Ration. Mech. Anal., 168 (2003), pp. 115-130. (Pubitemid 36931168)
-
(2003)
Archive for Rational Mechanics and Analysis
, vol.168
, Issue.2
, pp. 115-130
-
-
Rein, G.1
-
30
-
-
33645150332
-
A quasi-linear parabolic system of chemotaxis
-
23061
-
T. Senba and T. Suzuki, A quasi-linear parabolic system of chemotaxis, Abstr. Appl. Anal., (2006), 23061, 21 pp.
-
(2006)
Abstr. Appl. Anal.
-
-
Senba, T.1
Suzuki, T.2
-
31
-
-
34547418914
-
Global existence in sub-critical cases and finite time blow-up in super-critical cases to degenerate Keller-Segel systems
-
Y. Sugiyama, Global existence in sub-critical cases and finite time blow-up in super-critical cases to degenerate Keller-Segel systems, Differential Integral Equations, 19 (2006), pp. 841-876.
-
(2006)
Differential Integral Equations
, vol.19
, pp. 841-876
-
-
Sugiyama, Y.1
-
32
-
-
71249147604
-
E-regularity theorem and its application to the blow-up solutions of Keller-Segel systems in higher dimensions
-
Y. Sugiyama, e-regularity theorem and its application to the blow-up solutions of Keller-Segel systems in higher dimensions, J. Math. Anal. Appl., 364 (2010), pp. 51-70.
-
(2010)
J. Math. Anal. Appl.
, vol.364
, pp. 51-70
-
-
Sugiyama, Y.1
-
33
-
-
33646542023
-
Global existence and decay properties for a degenerate Keller-Segel model with a power factor in drift term
-
DOI 10.1016/j.jde.2006.03.003, PII S0022039606000921
-
Y. Sugiyama and H. Kunii, Global existence and decay properties for a degenerate Keller-Segel model with a power factor in drift term, J. Differential Equations, 227 (2006), pp. 333-364. (Pubitemid 43717480)
-
(2006)
Journal of Differential Equations
, vol.227
, Issue.1
, pp. 333-364
-
-
Sugiyama, Y.1
Kunii, H.2
-
34
-
-
77952551861
-
Aggregation vs. global diffusive behavior in the higher-dimensional Keller-Segel model
-
M. Winkler, Aggregation vs. global diffusive behavior in the higher-dimensional Keller-Segel model, J. Differential Equations, 248 (2010), pp. 2889-2905.
-
(2010)
J. Differential Equations
, vol.248
, pp. 2889-2905
-
-
Winkler, M.1
|