含血管生成的二维转移生长群体模型的数学分析
Mathematical analysis of a two-dimensional population model of metastatic growth including angiogenesis
摘要：
血管生成是肿瘤生长中的关键过程，其允许癌组织影响其脉管系统以改善营养物的供应和转移过程。在本文中，我们介绍了一个模型的转移，考虑到这一特点的密度。它是一个二维结构方程，速度场为零，边界上有一个源项。我们在这里提出的模型的数学分析，即方程的适定性和解的渐近行为，其自然规律性导致我们调查空间$\Wd(\Om)=\{V\in L^1;\;÷(GV)\in L^1\}$的一些基本性质，其中$G$是方程的速度场。
英文摘要：
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 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 $\Wd(\Om)=\{V\in L^1;\;÷(GV)\in L^1\}$, where $G$ is the velocity field of the equation.
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