论文标题
血管生成的双曲线 - 抛物性趋化趋化系统：全球动力学和放松限制对凯勒 - 塞格模型
The hyperbolic-parabolic chemotaxis system for vasculogenesis: global dynamics and relaxation limit toward a Keller-Segel model
论文作者
论文摘要
在关键的规律性设置中研究了描述血管网络形成的趋化聚集的Euler型双曲线促核系统。对于围绕恒定平衡状态的小初始数据，在均匀的混合空间中建立了全球经典解决方案对库奇问题的良好解决方案。然后，根据初始数据的额外规律性假设，分析了全局解决方案的最佳时间付费率。此外，双曲线 - 羟基蛋白酶系统的松弛极限（大摩擦极限）是合理的。结果表明，随着摩擦系数趋于零，双曲线 - 抛物性趋化性系统的全局解会收敛到具有显式收敛速率的凯勒 - 塞格方程的全局溶液。为了捕获非线性系统的耗散特性，我们的方法依赖于在低频中引入新的有效未知数，并在[5]中以Beauchard和Zuazua的精神构建Lyapunov功能来处理高频。
An Euler-type hyperbolic-parabolic system of chemotactic aggregation describing the vascular network formation is investigated in the critical regularity setting. For small initial data around a constant equilibrium state, the well-posedness of the global classical solution to the Cauchy problem with general pressure laws is established in homogeneous hybrid Besov spaces. Then, the optimal time-decay rates of the global solution are analyzed under an additional regularity assumption on the initial data. Furthermore, the relaxation limit (large friction limit) of the hyperbolic-parabolic system is justified rigorously. It is shown that as the friction coefficient tends to zero, the global solution of the hyperbolic-parabolic chemotaxis system converges to the global solution of the Keller-Segel equations with an explicit convergence rate. To capture the dissipative properties of the nonlinear system, our approach relies on the introduction of new effective unknowns in low frequencies and the construction of a Lyapunov functional in the spirit of Beauchard and Zuazua's in [5] to treat the high frequencies.
