Mathematical analysis of a two-dimensional population model of metastatic growth including angiogenesis

被引：10
|
作者：
Sebastien, Benzekry [1 ,2 ]
机构：
[1] Univ Provence, CMI LATP, UMR 6632, F-13453 Marseille 13, France
[2] Lab Toxicocinet & Pharmacocinet UMR MD3, F-13005 Marseille, France
来源：
JOURNAL OF EVOLUTION EQUATIONS | 2011年 / 11卷 / 01期
关键词：
2D Structured populations; Semigroup; Asymptotic behavior; Malthus parameter; Transport equation; TRACE THEOREMS; TUMOR-GROWTH;
D O I：
10.1007/s00028-010-0088-5
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
Angiogenesis is a key process in the tumoral growth which allows the cancerous tissue to impact on its vasculature in order to improve the nutrient's supply and the metastatic process. In this paper, we introduce a model for the density of metastasis which takes into account for this feature. It is a two-dimensional structured population equation with a vanishing velocity field and a source term on the boundary. We present here the mathematical analysis of the model, namely the well-posedness of the equation and the asymptotic behavior of the solutions, whose natural regularity led us to investigate some basic properties of the space where G is the velocity field of the equation.
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页码：187 / 213
页数：27
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