A Chemotaxis-Haptotaxis Model: The Roles of Nonlinear Diffusion and Logistic Source
A Chemotaxis-Haptotaxis Model: The Roles of Nonlinear Diffusion and Logistic Source
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DOI：
10.1137/100802943
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发表时间：
2011-03
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影响因子：
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通讯作者：
Youshan Tao;M. Winkler
中科院分区：
文献类型：
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作者：
Youshan Tao;M. Winkler
本文研究了肿瘤侵袭组织(细胞外基质)的趋化-趋化模型。该模型由描述癌细胞密度演化的抛物线趋化-趋触性PDE、控制基质降解酶浓度演化的抛物线PDE和反映ECM降解的ODE组成。根据Szymanska，Morales-Rodrigo，Lachowicz和Chaplane最近提出的方法[Math.模型、方法、应用科学，19(2009)，pp.257-281]，我们假设癌细胞通过ECM的迁移更像是在多孔介质中的运动。因此，我们认为癌细胞的自扩散系数$D(U)$是一个非线性函数，它推广了原型$D(U)=(u+1)^{m-1}$对于某个$m\geq1$。在假设(2n^2+4n-4)/(n^2+4n)$或$n+q9$和$m>；(2n^2+3n+2-\sqrt{8n(n+1)})/(n^2+2n)$(其中n表示空间维度)的情况下，在存在癌细胞密度的Logistic抑制的情况下，整体存在.
This paper deals with a chemotaxis-haptotaxis model of cancer invasion of tissue (extracellular matrix (ECM)). The model consists of a parabolic chemotaxis-haptotaxis PDE describing the evolution of cancer cell density, a parabolic PDE governing the evolution of matrix degrading enzyme concentration, and an ODE reflecting the degradation of ECM. Following a recent approach proposed by Szymanska, Morales-Rodrigo, Lachowicz, and Chaplain [Math. Models Methods Appl. Sci., 19 (2009), pp. 257–281], we assume that the migration of cancer cells through ECM is more like movement in a porous medium. Accordingly, we consider the self-diffusion coefficient $D(u)$ of cancer cells to be a nonlinear function generalizing the prototype $D(u)=(u+1)^{m-1}$ for some $m\geq1$. Under the assumption that either $n\leq8$ and $m>(2n^2+4n-4)/(n^2+4n)$, or $n\geq9$ and $m>(2n^2+3n+2-\sqrt{8n(n+1)})/(n^2+2n)$ (where n denotes the space dimension), and in the presence of logistic dampening of cancer cell densities, the global exist...