Analysis of Mathematical Models of Tumour Growth Incorporating Chemotaxis(<Special Topics>Reaction-Diffusion Models with Convective Terms)

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  • 走化性を伴う腫瘍成長モデルとその数理(<特集>移流項をもつ反応拡散系)
  • 走化性を伴う腫瘍成長モデルとその数理
  • ソウカセイ オ トモナウ シュヨウ セイチョウ モデル ト ソノ スウリ

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Abstract

In the field of Life and Biological Science, the understanding of tumour growth has made enormous progress in recent years. In this paper we study a couple of mathematical models of tumour angiogenesis with rigorous background to gain a mathematical characterization of tumour angiogenesis. One is proposed by Othmer and Stevens and developed by Levine and Sleeman, which has been arised in the theory of reinforced random walk. Another is considered by Anderson and Chaplain, based on a number of pathological and physiological researches. Mathematical analysis and characterization of these models are done by showing existence of global in time solution of the models and the asymptotic behaviour of them. Then we attempt to clarify the gap and equivalency between these models mathematically and investigate basic and essential mathematical properties common to them and pull out the relevance of these properties to angiogenesis.

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