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Volumn 12, Issue 6, 2011, Pages 3727-3740

Global weak solutions in a chemotaxis system with large singular sensitivity

Author keywords

Chemotaxis; Global existence; Singularity formation; Weak solutions

Indexed keywords

BLACK STAR; CHEMOTAXIS; GENERALIZED SOLUTION; GLOBAL EXISTENCE; GLOBAL WEAK SOLUTION; GLOBAL-IN-TIME SOLUTION; INTEGRAL ESTIMATE; NEUMANN PROBLEM; RADIALLY SYMMETRIC SOLUTION; SINGULARITY FORMATION; WEAK SOLUTION;

EID: 80052023588     PISSN: 14681218     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.nonrwa.2011.07.006     Document Type: Article
Times cited : (136)

References (23)
  • 1
    • 0014748565 scopus 로고
    • Initiation of slime mold aggregation viewed as an instability
    • E.F. Keller, and L.A. Segel Initiation of slime mold aggregation viewed as an instability J. Theor. Biol. 26 3 1970 399 415
    • (1970) J. Theor. Biol. , vol.26 , Issue.3 , pp. 399-415
    • Keller, E.F.1    Segel, L.A.2
  • 2
    • 63049107118 scopus 로고    scopus 로고
    • A users' guide to PDE models for chemotaxis
    • T. Hillen, and K. Painter A users' guide to PDE models for chemotaxis J. Math. Biol. 58 12 2009 183 217
    • (2009) J. Math. Biol. , vol.58 , Issue.12 , pp. 183-217
    • Hillen, T.1    Painter, K.2
  • 3
    • 4744373150 scopus 로고    scopus 로고
    • From 1970 until present: The KellerSegel model in chemotaxis and its consequences i
    • D. Horstmann From 1970 until present: the KellerSegel model in chemotaxis and its consequences I Jahresberichte DMV 105 3 2003 103 165
    • (2003) Jahresberichte DMV , vol.105 , Issue.3 , pp. 103-165
    • Horstmann, D.1
  • 4
    • 0015010990 scopus 로고
    • Traveling bands of chemotactic bacteria: A theoretical analysis
    • E.F. Keller, and L.A. Segel Traveling bands of chemotactic bacteria: a theoretical analysis J. Theor. Biol. 30 2 1971 235 248
    • (1971) J. Theor. Biol. , vol.30 , Issue.2 , pp. 235-248
    • Keller, E.F.1    Segel, L.A.2
  • 5
    • 0018181645 scopus 로고
    • Steady-state distribution of bacteria chemotactic toward oxygen
    • G. Rosen Steady-state distribution of bacteria chemotactic toward oxygen Bull. Math. Biol. 40 5 1978 671 674 (Pubitemid 9053191)
    • (1978) Bulletin of Mathematical Biology , vol.40 , Issue.5 , pp. 671-674
    • Rosen, G.1
  • 6
    • 0031207030 scopus 로고    scopus 로고
    • Aggregation, blowup, and collapse: The ABC'S of taxis in reinforced random walks
    • PII S0036139995288976
    • H.G. Othmer, and A. Stevens Aggregation, blowup and collapse: the ABC's of taxis in reinforced random walks SIAM J. Appl. Math. 57 4 1997 1044 1081 (Pubitemid 127642175)
    • (1997) SIAM Journal on Applied Mathematics , vol.57 , Issue.4 , pp. 1044-1081
    • Othmer, H.G.1    Stevens, A.2
  • 7
    • 0035307231 scopus 로고    scopus 로고
    • Partial differential equations of chemotaxis and angiogenesis
    • DOI 10.1002/mma.212
    • B.D. Sleeman, and H.A. Levine Partial differential equations of chemotaxis and angiogenesis Math. Meth. Appl. Sci. 24 6 2001 405 426 (Pubitemid 32371475)
    • (2001) Mathematical Methods in the Applied Sciences , vol.24 , Issue.6 , pp. 405-426
    • Sleeman, B.D.1    Levine, H.A.2
  • 8
    • 0031162898 scopus 로고    scopus 로고
    • A system of reaction diffusion equations arising in the theory of reinforced random walks
    • PII S0036139995291106
    • H.A. Levine, and B.D. Sleeman A system of reactiondiffusion equations arising in the theory of reinforced random walks SIAM J. Appl. Math. 57 3 1997 683 730 (Pubitemid 127639231)
    • (1997) SIAM Journal on Applied Mathematics , vol.57 , Issue.3 , pp. 683-730
    • Levine, H.A.1    Sleeman, B.D.2
  • 9
    • 0141644434 scopus 로고    scopus 로고
    • Finite dimensional attractors for one-dimensional KellerSegel equations
    • K. Osaki, and A. Yagi Finite dimensional attractors for one-dimensional KellerSegel equations Funkcialaj Ekvacioj 44 3 2001 441 469
    • (2001) Funkcialaj Ekvacioj , vol.44 , Issue.3 , pp. 441-469
    • Osaki, K.1    Yagi, A.2
  • 10
    • 0001580322 scopus 로고    scopus 로고
    • Global solutions to some parabolicelliptic systems of chemotaxis
    • P. Biler Global solutions to some parabolicelliptic systems of chemotaxis Adv. Math. Sci. Appl. 9 1 1999 347 359
    • (1999) Adv. Math. Sci. Appl. , vol.9 , Issue.1 , pp. 347-359
    • Biler, P.1
  • 11
    • 0005525169 scopus 로고    scopus 로고
    • Global existence of solutions to the parabolic systems of chemotaxis
    • T. Nagai, T. Senba, and K. Yoshida Global existence of solutions to the parabolic systems of chemotaxis RIMS Kokyuroku 1009 1997 22 28
    • (1997) RIMS Kokyuroku , vol.1009 , pp. 22-28
    • Nagai, T.1    Senba, T.2    Yoshida, K.3
  • 12
    • 78650780103 scopus 로고    scopus 로고
    • Global solutions in a fully parabolic chemotaxis system with singular sensitivity
    • M. Winkler Global solutions in a fully parabolic chemotaxis system with singular sensitivity Math. Meth. Appl. Sci. 34 2 2011 176 190
    • (2011) Math. Meth. Appl. Sci. , vol.34 , Issue.2 , pp. 176-190
    • Winkler, M.1
  • 14
    • 0005596499 scopus 로고    scopus 로고
    • Behavior of radially symmetric solutions of a system related to chemotaxis
    • PII S0362546X96002568
    • T. Nagai, and T. Senba Behavior of radially symmetric solutions of a system related to chemotaxis Nonlinear Anal. 30 6 1997 3837 3842 (Pubitemid 127407056)
    • (1997) Nonlinear Analysis, Theory, Methods and Applications , vol.30 , Issue.6 , pp. 3837-3842
    • Nagai, T.1    Senba, T.2
  • 16
    • 0000687738 scopus 로고    scopus 로고
    • Chemotactic collapse in a parabolic system of mathematical biology
    • T. Nagai, T. Senba, and T. Suzuki Chemotactic collapse in a parabolic system of mathematical biology Hiroshima Math. J. 30 3 2000 463 497
    • (2000) Hiroshima Math. J. , vol.30 , Issue.3 , pp. 463-497
    • Nagai, T.1    Senba, T.2    Suzuki, T.3
  • 17
    • 77958535262 scopus 로고    scopus 로고
    • Absence of collapse in a parabolic chemotaxis system with signal-dependent sensitivity
    • M. Winkler Absence of collapse in a parabolic chemotaxis system with signal-dependent sensitivity Math. Nachr. 283 11 2010 1664 1673
    • (2010) Math. Nachr. , vol.283 , Issue.11 , pp. 1664-1673
    • Winkler, M.1
  • 18
    • 18144371222 scopus 로고    scopus 로고
    • 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 1 2005 52 107 (Pubitemid 40621900)
    • (2005) Journal of Differential Equations , vol.215 , Issue.1 , pp. 52-107
    • Horstmann, D.1    Winkler, M.2
  • 19
    • 77952551861 scopus 로고    scopus 로고
    • Aggregation vs. global diffusive behavior in the higher-dimensional KellerSegel model
    • M. Winkler Aggregation vs. global diffusive behavior in the higher-dimensional KellerSegel model J. Differential Equations 248 12 2010 2889 2905
    • (2010) J. Differential Equations , vol.248 , Issue.12 , pp. 2889-2905
    • Winkler, M.1
  • 21
    • 0003306279 scopus 로고
    • NavierStokes equations. Theory and numerical analysis
    • North-Holland Amsterdam etc.
    • R. Temam NavierStokes equations. Theory and numerical analysis Studies in Mathematics and its Applications Vol. 2 1977 North-Holland Amsterdam etc.
    • (1977) Studies in Mathematics and Its Applications , vol.2
    • Temam, R.1
  • 22
    • 0035994224 scopus 로고    scopus 로고
    • An improved HardySobolev inequality and its application
    • N. Chaudhuri Adimurthi, and M. Ramaswamy An improved HardySobolev inequality and its application Proc. AMS 130 2 2002 489 505
    • (2002) Proc. AMS , vol.130 , Issue.2 , pp. 489-505
    • Adimurthi, N.C.1    Ramaswamy, M.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.