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Volumn 339, Issue 9, 2004, Pages 611-616

Optimal critical mass in the two dimensional Keller-Segel model in ℝ2;Masse critique optimale pour le modèle de Keller-Segel dans ℝ2

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EID: 18644382851     PISSN: 1631073X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.crma.2004.08.011     Document Type: Article
Times cited : (241)

References (19)
  • 1
    • 0000759151 scopus 로고
    • Sharp Sobolev inequalities on the sphere and the Moser-Trudinger inequality
    • W. Beckner Sharp Sobolev inequalities on the sphere and the Moser-Trudinger inequality Ann. Math. (2) 138 1 1993 213-242
    • (1993) Ann. Math. (2) , vol.138 , Issue.1 , pp. 213-242
    • Beckner, W.1
  • 2
    • 0010015506 scopus 로고
    • A class of nonlocal parabolic problems occurring in statistical mechanics
    • P. Biler T. Nadzieja A class of nonlocal parabolic problems occurring in statistical mechanics Colloq. Math. 66 1 1993 131-145
    • (1993) Colloq. Math. , vol.66 , Issue.1 , pp. 131-145
    • Biler, P.1    Nadzieja, T.2
  • 5
    • 26844499863 scopus 로고    scopus 로고
    • Global solutions of some chemotaxis and angiogenesis systems in high space dimensions
    • L. Corrias B. Perthame H. Zaag Global solutions of some chemotaxis and angiogenesis systems in high space dimensions Milan J. Math. 72 2004 1-29
    • (2004) Milan J. Math. , vol.72 , pp. 1-29
    • Corrias, L.1    Perthame, B.2    Zaag, H.3
  • 6
    • 0032445844 scopus 로고    scopus 로고
    • Global behaviour of a reaction-diffusion system modelling chemotaxis
    • H. Gajewski K. Zacharias Global behaviour of a reaction-diffusion system modelling chemotaxis Math. Nachr. 195 1998 77-114
    • (1998) Math. Nachr. , vol.195 , pp. 77-114
    • Gajewski, H.1    Zacharias, K.2
  • 7
    • 0000507343 scopus 로고    scopus 로고
    • Finite-time aggregation into a single point in a reaction-diffusion system
    • M.A. Herrero E. Medina J.J.L. Velázquez Finite-time aggregation into a single point in a reaction-diffusion system Nonlinearity 10 6 1997 1739-1754
    • (1997) Nonlinearity , vol.10 , Issue.6 , pp. 1739-1754
    • Herrero, M.A.1    Medina, E.2    Velázquez, J.J.L.3
  • 8
    • 0036581096 scopus 로고    scopus 로고
    • On the existence of radially symmetric blow-up solutions for the Keller-Segel model
    • D. Horstmann On the existence of radially symmetric blow-up solutions for the Keller-Segel model J. Math. Biol. 44 5 2002 463-478
    • (2002) J. Math. Biol. , vol.44 , Issue.5 , pp. 463-478
    • Horstmann, D.1
  • 9
    • 13844288282 scopus 로고    scopus 로고
    • From 1970 until now: The Keller-Segel model in chemotaxis and its consequences
    • D. Horstmann From 1970 until now: The Keller-Segel model in chemotaxis and its consequences Jahresber. Deutsch. Math.-Verei. 106 2004 51-69
    • (2004) Jahresber. Deutsch. Math.-Verei. , vol.106 , pp. 51-69
    • Horstmann, D.1
  • 10
    • 84966208077 scopus 로고
    • On explosions of solutions to a system of partial differential equations modelling chemotaxis
    • W. Jäger S. Luckhaus On explosions of solutions to a system of partial differential equations modelling chemotaxis Trans. Amer. Math. Soc. 329 2 1992 819-824
    • (1992) Trans. Amer. Math. Soc. , vol.329 , Issue.2 , pp. 819-824
    • Jäger, W.1    Luckhaus, S.2
  • 12
    • 26844509184 scopus 로고    scopus 로고
    • Applications of mathematical modelling to biological pattern formation
    • Coherent Structures in Complex Systems (Sitges, 2000) Springer Berlin
    • P.K. Maini Applications of mathematical modelling to biological pattern formation in: Coherent Structures in Complex Systems (Sitges, 2000) in: Lecture Notes in Phys. vol. 567 2001 Springer Berlin 205-217
    • (2001) Lecture Notes in Phys. , vol.567 , pp. 205-217
    • Maini, P.K.1
  • 13
    • 0344629886 scopus 로고    scopus 로고
    • Numerical simulation of chemotactic bacteria aggregation via mixed finite elements
    • A. Marrocco Numerical simulation of chemotactic bacteria aggregation via mixed finite elements Math. Model. Numer. Anal. (M2AN) 37 4 2003 617-630
    • (2003) Math. Model. Numer. Anal. (M2AN) , vol.37 , Issue.4 , pp. 617-630
    • Marrocco, A.1
  • 14
    • 14244268198 scopus 로고    scopus 로고
    • Mathematical Biology. II, Spatial Models and Biomedical Applications
    • third ed. New York: Springer-Verlag
    • J.D. Murray Mathematical Biology. II, Spatial Models and Biomedical Applications third ed. Interdisciplinary Appl. Math. vol. 18 2003 Springer-Verlag New York
    • (2003) Interdisciplinary Appl. Math. , vol.18
    • Murray, J.D.1
  • 15
    • 0001497848 scopus 로고    scopus 로고
    • Global existence and blow-up of radial solutions to a parabolic-elliptic system of chemotaxis
    • T. Nagai T. Senba Global existence and blow-up of radial solutions to a parabolic-elliptic system of chemotaxis Adv. Math. Sci. Appl. 8 1 1998 145-156
    • (1998) Adv. Math. Sci. Appl. , vol.8 , Issue.1 , pp. 145-156
    • Nagai, T.1    Senba, T.2
  • 16
    • 51249193541 scopus 로고
    • Random walk with persistence and external bias
    • C.S. Patlak Random walk with persistence and external bias B. Math. Biophys. 15 1953 311-338
    • (1953) B. Math. Biophys. , vol.15 , pp. 311-338
    • Patlak, C.S.1
  • 17
    • 0037053129 scopus 로고    scopus 로고
    • Weak solutions to a parabolic-elliptic system of chemotaxis
    • T. Senba T. Suzuki Weak solutions to a parabolic-elliptic system of chemotaxis J. Func. Anal. 47 2001 17-51
    • (2001) J. Func. Anal. , vol.47 , pp. 17-51
    • Senba, T.1    Suzuki, T.2
  • 18
    • 0036588873 scopus 로고    scopus 로고
    • Stability of some mechanisms of chemotactic aggregation
    • (electronic)
    • J.J.L. Velázquez Stability of some mechanisms of chemotactic aggregation SIAM J. Appl. Math. 62 5 2002 1581-1633 (electronic)
    • (2002) SIAM J. Appl. Math. , vol.62 , Issue.5 , pp. 1581-1633
    • Velázquez, J.J.L.1
  • 19
    • 0041473959 scopus 로고
    • Nonlinear Schrödinger equations and sharp interpolation estimates
    • M.I. Weinstein Nonlinear Schrödinger equations and sharp interpolation estimates Commun. Math. Phys. 87 4 1982/83 567-576
    • (1982) Commun. Math. Phys. , vol.87 , Issue.4 , pp. 567-576
    • Weinstein, M.I.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.