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Volumn 54, Issue 5, 2003, Pages 839-868

Blow-up and pattern formation in hyperbolic models for chemotaxis in 1-D

Author keywords

Blow up; Chemotaxis; Hyperbolic models

Indexed keywords


EID: 0141567903     PISSN: 00442275     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00033-003-3206-1     Document Type: Article
Times cited : (11)

References (26)
  • 1
    • 0000622777 scopus 로고    scopus 로고
    • Modelling the growth and form of capillary networks
    • J. C. McLachlan M. A. J. Chaplain, G. G. Singh, editor, Wiley
    • A. R. A. Anderson and M. A. J. Chaplain, Modelling the growth and form of capillary networks. In J. C. McLachlan M. A. J. Chaplain, G. G. Singh, editor, On Growth and Form: Spatio-Temporal Pattern Formation in Biology, Wiley, 1999, 225-249.
    • (1999) On Growth and Form: Spatio-Temporal Pattern Formation in Biology , pp. 225-249
    • Anderson, A.R.A.1    Chaplain, M.A.J.2
  • 2
    • 0001257097 scopus 로고    scopus 로고
    • A mathematical model for capillary network formation in the absence of endothelial cell proliferation
    • A. R. A. Anderson and M. A. J. Chaplain, A mathematical model for capillary network formation in the absence of endothelial cell proliferation. Appl. Math. Lett. 11 (1998), 109-116.
    • (1998) Appl. Math. Lett. , vol.11 , pp. 109-116
    • Anderson, A.R.A.1    Chaplain, M.A.J.2
  • 3
    • 0141723483 scopus 로고    scopus 로고
    • Cattaneo models for chemotaxis, numerical solution and pattern formation
    • Y. Dolak and T. Hillen, Cattaneo models for chemotaxis, numerical solution and pattern formation. J. Math. Biol. 46(2) (2003), 153-170.
    • (2003) J. Math. Biol. , vol.46 , Issue.2 , pp. 153-170
    • Dolak, Y.1    Hillen, T.2
  • 4
    • 0001767344 scopus 로고
    • Zur Theorie der Brownschen Bewegung
    • A. Einstein, Zur Theorie der Brownschen Bewegung. Annalen der Physik 19 (1906), 371381.
    • (1906) Annalen der Physik , vol.19 , pp. 371381
    • Einstein, A.1
  • 5
    • 0026133844 scopus 로고
    • Measurement of bacterial random motility and chemotaxis coefficients: II. Application of single cell based mathematical model
    • R. M. Ford and D. A. Lauffenburger, Measurement of bacterial random motility and chemotaxis coefficients: II. application of single cell based mathematical model. Biotechnol. Bioeng. 37 (1991), 661-672.
    • (1991) Biotechnol. Bioeng. , vol.37 , pp. 661-672
    • Ford, R.M.1    Lauffenburger, D.A.2
  • 6
    • 0026131334 scopus 로고
    • Measurement of bacterial random motility and chemotaxis coefficients: I. Stopped-flow diffusion chamber assay
    • R. M. Ford, B. R. Phillips, J. A. Quinn and D. A. Lauffenburger, Measurement of bacterial random motility and chemotaxis coefficients: I. stopped-flow diffusion chamber assay. Biotechnol. Bioeng. 37 (1991), 647-660.
    • (1991) Biotechnol. Bioeng. , vol.37 , pp. 647-660
    • Ford, R.M.1    Phillips, B.R.2    Quinn, J.A.3    Lauffenburger, D.A.4
  • 7
    • 0036057673 scopus 로고    scopus 로고
    • Hyperbolic models for chemosensitive movement
    • T. Hillen, Hyperbolic models for chemosensitive movement. Math. Models Methods Appl. Sci. 12(7) (2002), 1007-1034.
    • (2002) Math. Models Methods Appl. Sci. , vol.12 , Issue.7 , pp. 1007-1034
    • Hillen, T.1
  • 8
    • 0034917420 scopus 로고    scopus 로고
    • The diffusion limit of transport equations derived from velocity jump processes
    • T. Hillen and H. G. Othmer, The diffusion limit of transport equations derived from velocity jump processes. SIAM J. Appl. Math. 61(3) (2000), 751-775.
    • (2000) SIAM J. Appl. Math. , vol.61 , Issue.3 , pp. 751-775
    • Hillen, T.1    Othmer, H.G.2
  • 9
    • 0003120501 scopus 로고    scopus 로고
    • Existence of weak solutions for a hyperbolic model for chemosensitive movement
    • T. Hillen, C. Rohde, and F. Lutscher, Existence of weak solutions for a hyperbolic model for chemosensitive movement. J. Math. Anal. Appl. 260 (2001), 173-199.
    • (2001) J. Math. Anal. Appl. , vol.260 , pp. 173-199
    • Hillen, T.1    Rohde, C.2    Lutscher, F.3
  • 11
    • 84966208077 scopus 로고
    • On explosions of solutions to a system of partial differential equations modelling chemotaxis
    • W. Jäger and S. Luckhaus, On explosions of solutions to a system of partial differential equations modelling chemotaxis. Trans. AMS 329 (1992), 819-824.
    • (1992) Trans. AMS , vol.329 , pp. 819-824
    • Jäger, W.1    Luckhaus, S.2
  • 12
    • 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. Biology 26 (1970), 399-415.
    • (1970) J. Theor. Biology , vol.26 , pp. 399-415
    • Keller, E.F.1    Segel, L.A.2
  • 13
    • 0034845581 scopus 로고    scopus 로고
    • Mathematical modeling of capillary formation and development in tumor angiogenesis: Penetration into the stroma
    • H. A. Levine, S. Pamuk, B. D. Sleeman, and M. Nilsen-Hamilton, Mathematical modeling of capillary formation and development in tumor angiogenesis: Penetration into the stroma. Bull. Math. Biol. (2001), 801-863.
    • (2001) Bull. Math. Biol. , pp. 801-863
    • Levine, H.A.1    Pamuk, S.2    Sleeman, B.D.3    Nilsen-Hamilton, M.4
  • 14
    • 0031162898 scopus 로고    scopus 로고
    • A system of reaction diffusion equations arising in the theory of reinforced random walks
    • H. A. Levine and B. D. Sleeman, A system of reaction diffusion equations arising in the theory of reinforced random walks. SIAM J. Appl. Math. (1997), 683-730.
    • (1997) SIAM J. Appl. Math. , pp. 683-730
    • Levine, H.A.1    Sleeman, B.D.2
  • 15
    • 0033731143 scopus 로고    scopus 로고
    • A mathematical model for the roles of pericytes and macrophages in the onset of angiogenesis: I. The role of protease inhibitors in preventing angiogenesis
    • H. A. Levine, B. D. Sleeman, and M. Nilsen-Hamilton, A mathematical model for the roles of pericytes and macrophages in the onset of angiogenesis: I. the role of protease inhibitors in preventing angiogenesis. Math. Biosci. (2000), 77-115.
    • (2000) Math. Biosci. , pp. 77-115
    • Levine, H.A.1    Sleeman, B.D.2    Nilsen-Hamilton, M.3
  • 16
    • 0035287283 scopus 로고    scopus 로고
    • Mathematical modeling of the onset of capillary formation initiating angiogenesis
    • H. A. Levine, B. D. Sleeman, and M. Nilsen-Hamilton, Mathematical modeling of the onset of capillary formation initiating angiogenesis. J. Math. Biol. (2001), 195-238.
    • (2001) J. Math. Biol. , pp. 195-238
    • Levine, H.A.1    Sleeman, B.D.2    Nilsen-Hamilton, M.3
  • 17
    • 0031162898 scopus 로고    scopus 로고
    • A system of reaction diffusion equations arising in the theory of reinforced random walks
    • H. A. Levine and B. D. Sleeman, A system of reaction diffusion equations arising in the theory of reinforced random walks. SIAM J. Appl. Math. 57 (1997), 683-730.
    • (1997) SIAM J. Appl. Math. , vol.57 , pp. 683-730
    • Levine, H.A.1    Sleeman, B.D.2
  • 18
    • 0036725453 scopus 로고    scopus 로고
    • Modeling alignment and movement of animals and cells
    • F. Lutscher, Modeling alignment and movement of animals and cells. J. Math. Biol. 45 (2002), 234-260.
    • (2002) J. Math. Biol. , vol.45 , pp. 234-260
    • Lutscher, F.1
  • 20
    • 0036553052 scopus 로고    scopus 로고
    • The diffusion limit of transport equations (ii): Chemotaxis equations
    • H. G. Othmer and T. Hillen, The diffusion limit of transport equations (ii): Chemotaxis equations. SIAM J. Appl. Math. 62(4) (2002), 1122-1250.
    • (2002) SIAM J. Appl. Math. , vol.62 , Issue.4 , pp. 1122-1250
    • Othmer, H.G.1    Hillen, T.2
  • 21
    • 0141708727 scopus 로고
    • Oscillatory cAMP signaling in the development of dic-tyostelium discoideum
    • H. G. Othmer and P. Schaap, Oscillatory cAMP signaling in the development of dic- tyostelium discoideum. Comm. Theor. Biol. 89 (1990), 510 - 517.
    • (1990) Comm. Theor. Biol. , vol.89 , pp. 510-517
    • Othmer, H.G.1    Schaap, P.2
  • 22
    • 0031207030 scopus 로고    scopus 로고
    • Aggregation, blowup and collapse: The ABC's of taxis in reinforced random walks
    • H. G. Othmer and A. Stevens, Aggregation, blowup and collapse: The ABC's of taxis in reinforced random walks. SIAM J. Appl. Math. 57 (1997), 1044-1081.
    • (1997) SIAM J. Appl. Math. , vol.57 , pp. 1044-1081
    • Othmer, H.G.1    Stevens, A.2
  • 23
    • 51249193541 scopus 로고
    • Random walk with persistence and external bias
    • C. S. Patlak, Random walk with persistence and external bias. Bull. Math. Biophys. 15 (1953), 311-338.
    • (1953) Bull. Math. Biophys. , vol.15 , pp. 311-338
    • Patlak, C.S.1
  • 25
    • 0001595172 scopus 로고    scopus 로고
    • A theoretical study of receptor mechanisms in bacterial chemotaxis
    • L. A. Segel, A theoretical study of receptor mechanisms in bacterial chemotaxis. SIAM J. Appl. Math. 32 (1997), 653-665.
    • (1997) SIAM J. Appl. Math. , vol.32 , pp. 653-665
    • Segel, L.A.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.