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Volumn 33, Issue 1, 2010, Pages 12-24

Does a 'volume-filling effect' always prevent chemotactic collapse?

Author keywords

Blow up; Boundedness; Chemotaxis; Global existence

Indexed keywords

BLOW-UP; BOUNDED DOMAIN; BOUNDEDNESS; CELL DENSITY; CHEMOTACTIC COLLAPSE; CHEMOTAXIS MODEL; GLOBAL EXISTENCE; INFINITE TIME; NEUMANN BOUNDARY CONDITION; TECHNICAL CONDITIONS; TOTAL MASS;

EID: 73849129287     PISSN: 01704214     EISSN: 10991476     Source Type: Journal    
DOI: 10.1002/mma.1146     Document Type: Article
Times cited : (296)

References (28)
  • 1
    • 0014748565 scopus 로고
    • Initiation of slime mold aggregation viewed as an instability
    • Keller EF, Segel LA. Initiation of slime mold aggregation viewed as an instability. Journal of Theoretical Biology 1970; 26:399-415.
    • (1970) Journal of Theoretical Biology , vol.26 , pp. 399-415
    • Keller, E.F.1    Segel, L.A.2
  • 2
    • 63049107118 scopus 로고    scopus 로고
    • A user's guide to PDE models for Chemotaxis
    • Hillen T, Painter K. A user's guide to PDE models for Chemotaxis. Journal of Mathematical Biology 2009; 58(1-2):183-217.
    • (2009) Journal of Mathematical Biology , vol.58 , Issue.1-2 , pp. 183-217
    • Hillen, T.1    Painter, K.2
  • 3
    • 0000911252 scopus 로고
    • Blow-up of radially symmetric solutions to a Chemotaxis system
    • Nagai T. Blow-up of radially symmetric solutions to a Chemotaxis system. Advances in Mathematical Sciences and Applications 1995; 5:581-601.
    • (1995) Advances in Mathematical Sciences and Applications , vol.5 , pp. 581-601
    • Nagai, T.1
  • 4
    • 0010786688 scopus 로고    scopus 로고
    • Blowup of nonradial solutions to parabolic-elliptic systems modeling Chemotaxis in two-dimensional domains
    • Nagai T. Blowup of nonradial solutions to parabolic-elliptic systems modeling Chemotaxis in two-dimensional domains. Journal of Inequalities and Applications 2001; 6:37-55.
    • (2001) Journal of Inequalities and Applications , vol.6 , pp. 37-55
    • Nagai, T.1
  • 5
    • 84966208077 scopus 로고
    • On explosions of solutions to a system of partial differential equations modelling Chemotaxis
    • Jäger W, Luckhaus S. On explosions of solutions to a system of partial differential equations modelling Chemotaxis. Transactions of the American Mathematical Society 1992; 329:817-824.
    • (1992) Transactions of the American Mathematical Society , vol.329 , pp. 817-824
    • Jäger, W.1    Luckhaus, S.2
  • 6
    • 0031162898 scopus 로고    scopus 로고
    • A system of reaction diffusion equations arising in the theory of reinforced random walks
    • Levine HA, Sleeman D. A system of reaction diffusion equations arising in the theory of reinforced random walks. SIAM Journal on Applied Mathematics 1997; 57(3):683-730.
    • (1997) SIAM Journal on Applied Mathematics , vol.57 , Issue.3 , pp. 683-730
    • Levine, H.A.1    Sleeman, D.2
  • 10
    • 77952551861 scopus 로고    scopus 로고
    • Aggregation vs global diffusive behavior in the higher-dimensional Keller-Segel model
    • submitted
    • Winkler M. Aggregation vs global diffusive behavior in the higher-dimensional Keller-Segel model. Journal of Differential Equations, submitted.
    • Journal of Differential Equations
    • Winkler, M.1
  • 11
    • 73849149420 scopus 로고    scopus 로고
    • Finite time blow-up for a one-dimensional quasilinear parabolic-parabolic chemotaxis system
    • Preprint
    • Cieślak T, Laurencot PH. Finite time blow-up for a one-dimensional quasilinear parabolic-parabolic chemotaxis system. Preprint, 2009.
    • (2009)
    • Cieślak, T.1    Laurencot, P.H.2
  • 12
    • 0000687738 scopus 로고    scopus 로고
    • Chemotactic collapse in a parabolic system of mathematical biology
    • Nagai T, Senba T, Suzuki T. Chemotactic collapse in a parabolic system of mathematical biology. Hiroshima Mathematical Journal 2000; 30:463-497.
    • (2000) Hiroshima Mathematical Journal , vol.30 , pp. 463-497
    • Nagai, T.1    Senba, T.2    Suzuki, T.3
  • 13
    • 4744373150 scopus 로고    scopus 로고
    • From 1970 until present: The Keller-Segel model in chemotaxis and its consequences I
    • Horstmann D. From 1970 until present: the Keller-Segel model in chemotaxis and its consequences I. Jahresberichte der Deutsche Mathematiker Vereinigung 2003; 105(3):103-165.
    • (2003) Jahresberichte der Deutsche Mathematiker Vereinigung , vol.105 , Issue.3 , pp. 103-165
    • Horstmann, D.1
  • 14
    • 4944248574 scopus 로고    scopus 로고
    • Volume-filling and quorum-sensing in models for chemosensitive movement
    • Painter K, Hillen T. Volume-filling and quorum-sensing in models for chemosensitive movement. Canadian Applied Mathematics Quarterly 2002; 10(4):501-543.
    • (2002) Canadian Applied Mathematics Quarterly , vol.10 , Issue.4 , pp. 501-543
    • Painter, K.1    Hillen, T.2
  • 15
    • 0001404830 scopus 로고    scopus 로고
    • Global existence for a parabolic chemotaxis model with prevention of overcrowding
    • Hillen T, Painter KJ. Global existence for a parabolic chemotaxis model with prevention of overcrowding. Advances in Applied Mathematics 2001; 26:280-301.
    • (2001) Advances in Applied Mathematics , vol.26 , pp. 280-301
    • Hillen, T.1    Painter, K.J.2
  • 16
    • 33646266962 scopus 로고    scopus 로고
    • Long-time behaviour of solutions to a chemotaxis model with volume-filling effect
    • Wrzosek D. Long-time behaviour of solutions to a chemotaxis model with volume-filling effect. Proceedings of the Royal Society of Edinburgh 2006; 136A:431-444.
    • (2006) Proceedings of the Royal Society of Edinburgh , vol.136 A , pp. 431-444
    • Wrzosek, D.1
  • 17
    • 33746377577 scopus 로고    scopus 로고
    • Volume effects in the Keller-Segel model: Energy estimates preventing blow-up
    • Calvez V, Carrillo JA. Volume effects in the Keller-Segel model: energy estimates preventing blow-up. Journal de Mathmatiques Pures et Appliques 2006; 86:155-175.
    • (2006) Journal de Mathmatiques Pures et Appliques , vol.86 , pp. 155-175
    • Calvez, V.1    Carrillo, J.A.2
  • 19
    • 43049127974 scopus 로고    scopus 로고
    • Global existence of solutions to a chemotaxis system with volume filling effect
    • Cieślak T. Global existence of solutions to a chemotaxis system with volume filling effect. Colloquium Mathematicum 2008; 111(1):117-134.
    • (2008) Colloquium Mathematicum , vol.111 , Issue.1 , pp. 117-134
    • Cieślak, T.1
  • 20
    • 43049112453 scopus 로고    scopus 로고
    • Finite-time blow-up in a quasilinear system of chemotaxis
    • Cieślak T, Winkler M. Finite-time blow-up in a quasilinear system of chemotaxis. Nonlinearity 2008; 21:1057-1076.
    • (2008) Nonlinearity , vol.21 , pp. 1057-1076
    • Cieślak, T.1    Winkler, M.2
  • 21
  • 22
    • 0001205112 scopus 로고    scopus 로고
    • Application of the Trudinger-Moser inequality to a parabolic system of chemotaxis
    • Nagai T, Senba T, Yoshida K. Application of the Trudinger-Moser inequality to a parabolic system of chemotaxis. Funkcialaj Ekvacioj, International Series 1997; 40:411-433.
    • (1997) Funkcialaj Ekvacioj, International Series , vol.40 , pp. 411-433
    • Nagai, T.1    Senba, T.2    Yoshida, K.3
  • 23
    • 0025442951 scopus 로고
    • The role of critical exponents in blowup theorems
    • Levine HA. The role of critical exponents in blowup theorems. SIAM Reviews 1990; 32(2):262-288.
    • (1990) SIAM Reviews , vol.32 , Issue.2 , pp. 262-288
    • Levine, H.A.1
  • 24
    • 0010915457 scopus 로고    scopus 로고
    • Parabolic system of chemotaxis: Blowup in a finite and the infinite time
    • Senba T, Suzuki T. Parabolic system of chemotaxis: blowup in a finite and the infinite time. Methods and Applications of Analysis 2001; 8:349-367.
    • (2001) Methods and Applications of Analysis , vol.8 , pp. 349-367
    • Senba, T.1    Suzuki, T.2
  • 25
    • 0032445844 scopus 로고    scopus 로고
    • Global behavior of a reaction-diffusion system modelling chemotaxis
    • Gajewski H, Zacharias K. Global behavior of a reaction-diffusion system modelling chemotaxis. Mathematische Nachrichten 1998; 195:77-114.
    • (1998) Mathematische Nachrichten , vol.195 , pp. 77-114
    • Gajewski, H.1    Zacharias, K.2
  • 27
    • 0001742516 scopus 로고
    • Dynamic theory of quasilinear parabolic systems III global existence
    • Amann H. Dynamic theory of quasilinear parabolic systems III global existence. Mathematische Zeitschrift 1989; 202:219-250.
    • (1989) Mathematische Zeitschrift , vol.202 , pp. 219-250
    • Amann, H.1
  • 28
    • 33750624355 scopus 로고    scopus 로고
    • Quasilinear nonuniformly parabolic system modelling chemotaxis
    • Cieślak T. Quasilinear nonuniformly parabolic system modelling chemotaxis. Journal of Mathematical Analysis and Applications 2007; 326(2): 1410-1426.
    • (2007) Journal of Mathematical Analysis and Applications , vol.326 , Issue.2 , pp. 1410-1426
    • Cieślak, T.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.