论文标题
在多维中，趋化趋化性系统的较大时间行为和扩散极限
Large Time Behavior and Diffusion Limit for a System of Balance Laws From Chemotaxis in Multi-dimensions
论文作者
论文摘要
我们考虑了cauchy问题的平衡法系统，该系统从趋化模型中得出，在多个空间维度中具有奇异灵敏度。利用能量方法，我们首先证明，当只有一阶空间衍生物的能量的初始数据的能量足够小时，经典解决方案的全球适合性是凯奇问题的全球辅助性，并且显示溶液会融合到规定的恒定恒定平衡状态，因为随着时间的流逝，溶液会趋于无限。然后，我们证明，当化学扩散系数趋于零时，完全耗散模型的溶液会收敛到相应的部分耗散模型的溶液。
We consider the Cauchy problem for a system of balance laws derived from a chemotaxis model with singular sensitivity in multiple space dimensions. Utilizing energy methods, we first prove the global well-posedness of classical solutions to the Cauchy problem when only the energy of the first order spatial derivatives of the initial data is sufficiently small, and the solutions are shown to converge to the prescribed constant equilibrium states as time goes to infinity. Then we prove that the solutions of the fully dissipative model converge to those of the corresponding partially dissipative model when the chemical diffusion coefficient tends to zero.
