一类化学趋向性平衡律系统的初值和边值问题:全局动力学和扩散极限

Zefu Feng
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引用次数: 2

摘要

. 本文研究了具有对数灵敏度和非线性生产/降解率的趋化性模型引起的平衡律系统的长时间动力学和大数据解的扩散极限。利用能量方法,我们证明了在时变Dirichlet边界条件下,解的长时间动力学是由边界数据驱动的,并且对初始能量的大小没有限制。此外,在零Dirichlet边界条件下建立了零化学扩散极限,这在以往的相关模型研究中没有观察到
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Initial and Boundary Value Problem for a System of Balance Laws from Chemotaxis: Global Dynamics and Diffusivity Limit
. In this paper, we study long-time dynamics and diffusion limit of large-data solutions to a system of balance laws arising from a chemotaxis model with logarithmic sensitivity and nonlinear production/degradation rate. Utilizing energy methods, we show that under time-dependent Dirichlet boundary conditions, long-time dynamics of solutions are driven by their boundary data, and there is no restriction on the magnitude of initial energy. Moreover, the zero chemical diffusivity limit is established under zero Dirichlet boundary conditions, which has not been observed in previous studies on related models
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