Mathematical models of tumour angiogenesis

Akisato Kubo, Takashi Suzuki

Research output: Contribution to journalArticle

16 Citations (Scopus)

Abstract

We first study a parabolic-ODE system modelling tumour growth proposed by Othmer and Stevens [Aggregation, blowup, and collapse: the ABC's of taxis in reinforced random walks, SIAM J. Appl. Math. 57 (4) (1997) 1044-1081]. According to Levine and Sleeman [A system of reaction and diffusion equations arising in the theory of reinforced random walks, SIAM J. Appl. Math. 57 (3) (1997) 683-730], we reduced it to a hyperbolic equation and showed the existence of collapse in [A. Kubo, T. Suzuki, Asymptotic behavior of the solution to a parabolic ODE system modeling tumour growth, Differential Integral Equations 17 (2004) 721-736]. We also deal with the system in case the reduced equation is elliptic and show the existence of collapse analogously. Next we apply the above result to another model proposed by Anderson and Chaplain arising from tumour angiogenesis and show the existence of collapse. Further we investigate a contact point between these two models and a common property to them.

Original languageEnglish
Pages (from-to)48-55
Number of pages8
JournalJournal of Computational and Applied Mathematics
Volume204
Issue number1
DOIs
Publication statusPublished - 01-07-2007

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Angiogenesis
Tumors
Tumor
Reinforced Random Walk
Mathematical Model
Mathematical models
Tumor Growth
System Modeling
Point contacts
Integral-differential Equation
Integral equations
Agglomeration
Hyperbolic Equations
Diffusion equation
Blow-up
Aggregation
Asymptotic Behavior
Contact
Model

All Science Journal Classification (ASJC) codes

  • Computational Mathematics
  • Applied Mathematics

Cite this

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Mathematical models of tumour angiogenesis. / Kubo, Akisato; Suzuki, Takashi.

In: Journal of Computational and Applied Mathematics, Vol. 204, No. 1, 01.07.2007, p. 48-55.

Research output: Contribution to journalArticle

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