메뉴 건너뛰기




Volumn 8, Issue 2, 2008, Pages 353-378

Local existence and finite time blow-up of solutions in the 2-D Keller-Segel system

Author keywords

Blow up; Blow up rate; Keller Segel system; Local and global existence

Indexed keywords


EID: 44549087932     PISSN: 14243199     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00028-008-0375-6     Document Type: Article
Times cited : (57)

References (22)
  • 1
    • 21844518574 scopus 로고
    • Remarks on the preceding paper by M. Ben-Artzi, "Global solutions of two-dimensional Navier-Stokes and Euler equations
    • BREZIS, H., Remarks on the preceding paper by M. Ben-Artzi, "Global solutions of two-dimensional Navier-Stokes and Euler equations", Arch. Rational Mech. Anal., 128 (1994), 359-360.
    • (1994) Arch. Rational Mech. Anal , vol.128 , pp. 359-360
    • BREZIS, H.1
  • 2
    • 26844499863 scopus 로고    scopus 로고
    • Global Solutions of Some Chemotaxis and Angiogenesis Systems in High Space Dimensions
    • CORRIAS, L., PERTHAME, B. and ZAAG, H., Global Solutions of Some Chemotaxis and Angiogenesis Systems in High 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
  • 3
    • 0019784884 scopus 로고
    • Nonlinear aspects of chemotaxis
    • CHILDRESS, S. and PERCUS, J. K., Nonlinear aspects of chemotaxis, Math. Biosci., 56 (1981), 217-237.
    • (1981) Math. Biosci , vol.56 , pp. 217-237
    • CHILDRESS, S.1    PERCUS, J.K.2
  • 6
    • 0039712703 scopus 로고    scopus 로고
    • Singularity patterns in a chemotaxis model
    • HERRERO, M. A. and VELÁZQUEZ, J. L., Singularity patterns in a chemotaxis model, Math. Ann., 36 (1996), 583-623.
    • (1996) Math. Ann , vol.36 , pp. 583-623
    • HERRERO, M.A.1    VELÁZQUEZ, J.L.2
  • 8
    • 0030334089 scopus 로고    scopus 로고
    • Chemotactic collapse for the Keller-Segel model
    • HERRERO, M. A. and VELÁZQUEZ, J. L., Chemotactic collapse for the Keller-Segel model, J. Math. Biol., 35 (1996), 177-194.
    • (1996) J. Math. Biol , vol.35 , pp. 177-194
    • HERRERO, M.A.1    VELÁZQUEZ, J.L.2
  • 9
    • 44549085505 scopus 로고    scopus 로고
    • HORSTMANN, D., From 1970 until present: the Keller-Segel model in chemotaxis and its consequences.I., I.Jahresber.Deutsch.Math.- Verein., 105 (2003), 103-165.
    • HORSTMANN, D., From 1970 until present: the Keller-Segel model in chemotaxis and its consequences.I., I.Jahresber.Deutsch.Math.- Verein., 105 (2003), 103-165.
  • 10
    • 84966208077 scopus 로고
    • On explosions of solutions to a system of partial differential equations modelling chemotaxis
    • JÄGER, W. and LUCKHAUS, S., On explosions of solutions to a system of partial differential equations modelling chemotaxis, Trans. Amer. Math. Soc., 329 (1992), 819-824.
    • (1992) Trans. Amer. Math. Soc , vol.329 , pp. 819-824
    • JÄGER, W.1    LUCKHAUS, S.2
  • 11
    • 0014748565 scopus 로고
    • Initiation of slime mold aggregation viewed as an instability
    • KELLER, E. F. and SEGEL, L. A., 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.F.1    SEGEL, L.A.2
  • 12
    • 77954168108 scopus 로고    scopus 로고
    • Strong solutions of the Keller-Segel system with weak L n/2 initial data and its application to the blow-up rate
    • to appear in
    • KOZONO, H. and SUGIYAMA, Y., Strong solutions of the Keller-Segel system with weak L n/2 initial data and its application to the blow-up rate, to appear in Math. Nachr.
    • Math. Nachr
    • KOZONO, H.1    SUGIYAMA, Y.2
  • 13
    • 25844459072 scopus 로고    scopus 로고
    • Finite time blow-up of the solution for the nonlinear parabolic equation of the drift diffusion type
    • KUROKIBA, M. and OGAWA, T., Finite time blow-up of the solution for the nonlinear parabolic equation of the drift diffusion type, Differential and Integral Equations, 16 (2003), 427-452.
    • (2003) Differential and Integral Equations , vol.16 , pp. 427-452
    • KUROKIBA, M.1    OGAWA, T.2
  • 14
    • 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, Adv. Math. Sci. Appl., 5 (1995), 581-601.
    • (1995) Adv. Math. Sci. Appl , vol.5 , pp. 581-601
    • NAGAI, T.1
  • 15
    • 0001205112 scopus 로고    scopus 로고
    • Application of the Moser-Trudinger inequality to a parabolic system of chemotaxis, Funkc
    • NAGAI, T., SENBA, T. and YOSHIDA, K., Application of the Moser-Trudinger inequality to a parabolic system of chemotaxis, Funkc. Ekvacioj, 40 (1997), 411-433.
    • (1997) Ekvacioj , vol.40 , pp. 411-433
    • NAGAI, T.1    SENBA, T.2    YOSHIDA, K.3
  • 16
    • 10244221915 scopus 로고    scopus 로고
    • Behavior of solutions to a parabolic system modeling chemotaxis
    • NAGAI, T., Behavior of solutions to a parabolic system modeling chemotaxis, J. Korean Math. Soc., 37 (2000), 721-733.
    • (2000) J. Korean Math. Soc , vol.37 , pp. 721-733
    • NAGAI, T.1
  • 17
    • 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, J. Inequal. Appl., 6 (2001), 37-55.
    • (2001) J. Inequal. Appl , vol.6 , pp. 37-55
    • NAGAI, T.1
  • 18
    • 0010915457 scopus 로고    scopus 로고
    • Parabolic system of chemotaxis: Blowup in a finite and the infinite time
    • SENBA, T. and SUZUKI, T., Parabolic system of chemotaxis: blowup in a finite and the infinite time, Met. Appl. Ana., 8 (2001), 349-368.
    • (2001) Met. Appl. Ana , vol.8 , pp. 349-368
    • SENBA, T.1    SUZUKI, T.2
  • 19
    • 0003201639 scopus 로고
    • Singular integrals and differentiability properties of functions
    • Princeton University Press, Princeton, N.J
    • STEIN, E. M., Singular integrals and differentiability properties of functions, Princeton Mathematical Series, No.30 Princeton University Press, Princeton, N.J. (1970).
    • (1970) Princeton Mathematical Series , vol.30
    • STEIN, E.M.1
  • 20
    • 33646542023 scopus 로고    scopus 로고
    • Global existence and decay properties for a degenerate Keller-Segel model with a power factor in drift term
    • SUGIYAMA, Y. and KUNII, H., Global existence and decay properties for a degenerate Keller-Segel model with a power factor in drift term, J. Differential Equations 227, 333-364, (2006).
    • (2006) J. Differential Equations , vol.227 , pp. 333-364
    • SUGIYAMA, Y.1    KUNII, H.2
  • 21
    • 34547418914 scopus 로고    scopus 로고
    • Global existence in sub-critical cases and finite time blow-up in super-critical cases to degenerate Keller-Segel systems
    • SUGIYAMA, Y., Global existence in sub-critical cases and finite time blow-up in super-critical cases to degenerate Keller-Segel systems, Diff. Integral Equations 9 (2006), 841-876.
    • (2006) Diff. Integral Equations , vol.9 , pp. 841-876
    • SUGIYAMA, Y.1
  • 22
    • 0001488448 scopus 로고    scopus 로고
    • Norm behavior of solutions to a parabolic system of chemotaxis
    • YAGI, A., Norm behavior of solutions to a parabolic system of chemotaxis, Math. Japonica, 45 (1997), 241-265.
    • (1997) Math. Japonica , vol.45 , pp. 241-265
    • YAGI, A.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.