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Volumn 70, Issue 2, 2005, Pages 221-240

Global existence and blow-up for the solutions to nonlinear parabolic-elliptic system modelling chemotaxis

Author keywords

Blow up; Chemotaxis; Global existence; Keller Segel model; Parabolic elliptic system

Indexed keywords

AGGLOMERATION; BOUNDARY CONDITIONS; ESTIMATION; INTEGRAL EQUATIONS; THEOREM PROVING;

EID: 17644413806     PISSN: 02724960     EISSN: None     Source Type: Journal    
DOI: 10.1093/imamat/hxh032     Document Type: Article
Times cited : (11)

References (19)
  • 1
    • 0000163462 scopus 로고
    • Existence and asymptotics of solutions for a parabolic-elliptic system with nonlinear no-flux boundary conditions
    • Biler, P. (1992) Existence and asymptotics of solutions for a parabolic-elliptic system with nonlinear no-flux boundary conditions. Nonlinear Anal. TMA, 19, 1121-1136.
    • (1992) Nonlinear Anal. TMA , vol.19 , pp. 1121-1136
    • Biler, P.1
  • 2
    • 0000531920 scopus 로고
    • Existence and nonexistence of solutions for a model of gravitational in interaction of particles, I
    • Biler, P. & Nadzieja, T. (1994) Existence and nonexistence of solutions for a model of gravitational in interaction of particles, I. Colloq. Math., 66, 319-334.
    • (1994) Colloq. Math. , vol.66 , pp. 319-334
    • Biler, P.1    Nadzieja, T.2
  • 4
    • 17644400039 scopus 로고    scopus 로고
    • Existence and uniqueness of solutions to nonlinear parabolic-elliptic type chemotaxis system
    • J. Wuhan University (Natural Science Edition), to appear
    • Chen, H. & Zhong, X.-H. (2004) Existence and uniqueness of solutions to nonlinear parabolic-elliptic type chemotaxis system. J. Wuhan University (Natural Science Edition), to appear.
    • (2004)
    • Chen, H.1    Zhong, X.-H.2
  • 5
    • 0019784884 scopus 로고
    • Nonlinear aspects of chemotaxis
    • Childress, S. & Percus, J. K. (1981) Nonlinear aspects of chemotaxis. Math. Biosci., 56, 217-237.
    • (1981) Math. Biosci. , vol.56 , pp. 217-237
    • Childress, S.1    Percus, J.K.2
  • 6
    • 84966208077 scopus 로고
    • On explosions of solutions to a system of partial differential equations modelling chemotaxis
    • Jäger, W. & Luckhaus, S. (1992) On explosions of solutions to a system of partial differential equations modelling chemotaxis. Trans. Amer. Math. Soc., 329, 819-824.
    • (1992) Trans. Amer. Math. Soc. , vol.329 , pp. 819-824
    • Jäger, W.1    Luckhaus, S.2
  • 7
    • 0014748565 scopus 로고
    • Initiation of slime mold aggregation viewed as an instability
    • Keller, E. F. & 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 , pp. 399-415
    • Keller, E.F.1    Segel, L.A.2
  • 8
    • 0000911252 scopus 로고
    • Blow-up of radially symmetric solutions to a chemotaxis system
    • Gakkōtosho, Tokyo
    • Nagai, T. (1995) Blow-up of radially symmetric solutions to a chemotaxis system. Adv. Math. Sci. Appl. Gakkōtosho, Tokyo, 5, 581-601.
    • (1995) Adv. Math. Sci. Appl. , vol.5 , pp. 581-601
    • Nagai, T.1
  • 9
    • 10244221915 scopus 로고    scopus 로고
    • Behavior of solutions to a parabolic-elliptic system modelling chemotaxis
    • Nagai, T. (2000) Behavior of solutions to a parabolic-elliptic system modelling chemotaxis. J. Korean Math. Soc., 37, 721-733.
    • (2000) J. Korean Math. Soc. , vol.37 , pp. 721-733
    • Nagai, T.1
  • 10
    • 0010786688 scopus 로고    scopus 로고
    • Blowup of nonradial solutions to parabolic-elliptic systems modeling chemotaxis in two- dimensional domains
    • Nagai, T. (2001) Blowup of nonradial solutions to parabolic-elliptic systems modeling chemotaxis in two- dimensional domains. J. Inequal. Appl., 6, 37-55.
    • (2001) J. Inequal. Appl. , vol.6 , pp. 37-55
    • Nagai, T.1
  • 11
    • 0001497848 scopus 로고    scopus 로고
    • Global existence and blow-up of radial solutions to a parabolic-elliptic system of chemotaxis
    • Gakkōtosho, Tokyo
    • Nagai, T. & Senba, T. (1998) Global existence and blow-up of radial solutions to a parabolic-elliptic system of chemotaxis. Adv. Math. Sci. Appl. Gakkōtosho, Tokyo, 8, 145-160.
    • (1998) Adv. Math. Sci. Appl. , vol.8 , pp. 145-160
    • Nagai, T.1    Senba, T.2
  • 12
    • 0001205112 scopus 로고    scopus 로고
    • Application of the Trudinger-Moser inequality to a parabolic system of chemotaxis
    • Nagai, T., Senba, T. & Yoshida, K. (1997) Application of the Trudinger-Moser inequality to a parabolic system of chemotaxis. Funkcialaj Ekvacioj, 40, 411-433.
    • (1997) Funkcialaj Ekvacioj , vol.40 , pp. 411-433
    • Nagai, T.1    Senba, T.2    Yoshida, K.3
  • 13
    • 0015757937 scopus 로고
    • Chemotaxis, signal relaying, and aggregation morphology
    • Nanjundiah, V. (1973) Chemotaxis, signal relaying, and aggregation morphology. J. Theor. Biol., 42, 63-105.
    • (1973) J. Theor. Biol. , vol.42 , pp. 63-105
    • Nanjundiah, V.1
  • 14
    • 0001928261 scopus 로고    scopus 로고
    • Blow-up of radially symmetric solutions to some systems of partial differential equations modelling chemotaxis
    • Gakkōtosho, Tokyo
    • Senba, T. (1997) Blow-up of radially symmetric solutions to some systems of partial differential equations modelling chemotaxis. Adv. Math. Sci. Appl. Gakkōtosho, Tokyo, 7, 79-92.
    • (1997) Adv. Math. Sci. Appl. , vol.7 , pp. 79-92
    • Senba, T.1
  • 15
    • 0041437511 scopus 로고    scopus 로고
    • Local and norm behavior of blow up solutions to a parabolic system of chemotaxis
    • Senba, T. & Suzuki, T. (2000) Local and norm behavior of blow up solutions to a parabolic system of chemotaxis. J. Korean Math. Soc. 37, 929-941.
    • (2000) J. Korean Math. Soc. , vol.37 , pp. 929-941
    • Senba, T.1    Suzuki, T.2
  • 16
    • 0002819277 scopus 로고    scopus 로고
    • Chemotactic collapse in a parabolic-elliptic system of mathematical biology
    • Senba, T. & Suzuki, T. (2001) Chemotactic collapse in a parabolic-elliptic system of mathematical biology. Adv. Diff. Eqns 6, 21-50.
    • (2001) Adv. Diff. Eqns. , vol.6 , pp. 21-50
    • Senba, T.1    Suzuki, T.2
  • 17
    • 21144461798 scopus 로고
    • On steady distributions of self-attracting clusters under friction and fluctuations
    • Wolansky, G. (1992a) On steady distributions of self-attracting clusters under friction and fluctuations. Arch. Rational Mech. Anal., 119, 355-391.
    • (1992) Arch. Rational Mech. Anal. , vol.119 , pp. 355-391
    • Wolansky, G.1
  • 18
    • 51249166872 scopus 로고
    • On the evolution of self-interacting clusters and applications to semilinear equations with exponential nonlinearity
    • Wolansky, G. (1992b) On the evolution of self-interacting clusters and applications to semilinear equations with exponential nonlinearity. J. Analyse Math., 59, 251-272.
    • (1992) J. Analyse Math. , vol.59 , pp. 251-272
    • Wolansky, G.1
  • 19
    • 17644397750 scopus 로고    scopus 로고
    • Norm behavior of solutions to the parabolic system of chemotaxis
    • to appear
    • Yagi, A. Norm behavior of solutions to the parabolic system of chemotaxis. Math. Japonica, to appear.
    • Math. Japonica
    • Yagi, A.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.