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Volumn 204, Issue 1, 2007, Pages 48-55

Mathematical models of tumour angiogenesis

Author keywords

Anderson Chaplain model; Collapse; Othmer Stevens model; Parabolic ODE system; Tumour angiogenesis

Indexed keywords

DIFFERENTIAL EQUATIONS; INTEGRAL EQUATIONS; MATHEMATICAL MODELS; TUMORS;

EID: 34047250625     PISSN: 03770427     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cam.2006.04.027     Document Type: Article
Times cited : (20)

References (10)
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    • Anderson A.R.A., and Chaplain M.A.J. A mathematical model for capillary network formation in the absence of endothelial cell proferation. Appl. Math. Lett. 11 3 (1998) 109-114
    • (1998) Appl. Math. Lett. , vol.11 , Issue.3 , pp. 109-114
    • Anderson, A.R.A.1    Chaplain, M.A.J.2
  • 2
    • 0032170064 scopus 로고    scopus 로고
    • Continuous and discrete mathematical models of tumour-induced angiogenesis
    • Anderson A.R.A., and Chaplain M.A.J. Continuous and discrete mathematical models of tumour-induced angiogenesis. Bull. Math. Bio. 60 (1998) 857-899
    • (1998) Bull. Math. Bio. , vol.60 , pp. 857-899
    • Anderson, A.R.A.1    Chaplain, M.A.J.2
  • 4
    • 34047256892 scopus 로고    scopus 로고
    • Asymptotic behavior of the solution to a parabolic ODE system modeling tumour growth
    • Kubo A., and Suzuki T. Asymptotic behavior of the solution to a parabolic ODE system modeling tumour growth. Differential Integral Equations 17 (2004) 721-736
    • (2004) Differential Integral Equations , vol.17 , pp. 721-736
    • Kubo, A.1    Suzuki, T.2
  • 5
    • 34047258738 scopus 로고    scopus 로고
    • A mathematical approach to Othmer-Stevens model
    • Kubo A., and Suzuki T. A mathematical approach to Othmer-Stevens model. Wseas Trans. Biol. Biomed. 2 1 (2005) 45-50
    • (2005) Wseas Trans. Biol. Biomed. , vol.2 , Issue.1 , pp. 45-50
    • Kubo, A.1    Suzuki, T.2
  • 6
    • 0031162898 scopus 로고    scopus 로고
    • A system of reaction and diffusion equations arising in the theory of reinforced random walks
    • Levine H.A., and Sleeman B.D. A system of reaction and diffusion equations arising in the theory of reinforced random walks. SIAM J. Appl. Math. 57 3 (1997) 683-730
    • (1997) SIAM J. Appl. Math. , vol.57 , Issue.3 , pp. 683-730
    • Levine, H.A.1    Sleeman, B.D.2
  • 7
    • 0031207030 scopus 로고    scopus 로고
    • Aggregation, blowup, and collapse: the ABC's of taxis in reinforced random walks
    • Othmer H.G., and Stevens A. Aggregation, blowup, and collapse: the ABC's of taxis in reinforced random walks. SIAM J. Appl. Math. 57 4 (1997) 1044-1081
    • (1997) SIAM J. Appl. Math. , vol.57 , Issue.4 , pp. 1044-1081
    • Othmer, H.G.1    Stevens, A.2
  • 8
    • 0000189791 scopus 로고    scopus 로고
    • A mathematical analysis of a model for capillary network formation in the absence of endothelial cell proliferation
    • Sleeman B.D., Anderson A.R.A., and Chaplain M.A.J. A mathematical analysis of a model for capillary network formation in the absence of endothelial cell proliferation. Appl. Math. Lett. 12 (1999) 121-127
    • (1999) Appl. Math. Lett. , vol.12 , pp. 121-127
    • Sleeman, B.D.1    Anderson, A.R.A.2    Chaplain, M.A.J.3
  • 9
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    • Partial differential equations of chemotaxis and angiogenesis
    • Sleeman B.D., and Levine H.A. Partial differential equations of chemotaxis and angiogenesis. Math. Methods Appl. Sci. 24 (2002) 405-426
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    • Sleeman, B.D.1    Levine, H.A.2
  • 10
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    • On existence and non-existence of global solutions to a system of reaction-diffusion equations modeling chemotaxis
    • Yang Y., Chen H., and Liu W. On existence and non-existence of global solutions to a system of reaction-diffusion equations modeling chemotaxis. SIAM J. Math. Anal. 33 (2001) 736-785
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* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.