Asymptotic Analysis of a Chemotaxis System with Non-Diffusive Memory
Asymptotic Analysis of a Chemotaxis System with Non-Diffusive Memory
复制标题
非扩散记忆趋化系统的渐近分析
DOI：
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发表时间：
2012
期刊：
影响因子：
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通讯作者：
J. Velázquez
中科院分区：
文献类型：
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作者：
A. Stevens;J. Velázquez
本文详细计算了具有与 ODE 耦合的对数趋化敏感性的趋化方程的长时间渐近。我们考虑任意空间维度的径向对称设置。 ODE 描述了一种非扩散化学物质，它是由趋化物质本身产生的。直观上，该模型可以与许多粒子的自吸引强化随机游走相关。因此，与经典的 Keller-Segel 模型相比，该系统的行为在全局解的存在以及有限或无限时间爆炸的发生方面存在显着差异。在目前的情况下，爆炸更有可能发生在较低维度。除其他外，该 PDE-ODE 系统在文献中用于模拟趋触性和血管生成。
In this paper detailed long time asymptotics are calculated for a chemotaxis equation with a logarithmic chemotactic sensitivity which is coupled to an ODE. We consider the radial symmetric setting in any space dimension. The ODE describes a non-diffusing chemical, which is produced by the chemotactic species itself. Intuitively this model can be related to self-attracting reinforced random walks for many particles. Thus the behavior of this system crucially differs with respect to existence of global solutions and the occurrence of finite or infinite time blow-up if compared to the classical Keller-Segel model. Blow-up is more likely to happen in lower dimensions in the present case. This PDE-ODE system is, among others, used in the literature to model haptotaxis and angiogenesis.
影响因子：
1.7
作者：
Brenner, MP;Constantin, P;Venkataramani, SC
通讯作者：
Venkataramani, SC