论文标题
非局部反应阻止趋化性的超临界情况
Nonlocal reaction preventing blow-up in the supercritical case of chemotaxis
论文作者
论文摘要
本文研究了有界域中具有非局部非线性源的凯勒 - 塞格模型的非负溶液。聚集和非局部反应项之间的竞争被突出显示：当生长因子强于衰减效应时，借助非局部项，该模型承认了经典的解决方案，该解决方案均匀地界定。此外，当生长因子与衰减效应相比相同时，非本地非线性指数可以防止趋化性崩溃。对于适当的指数范围以及与恒定平衡状态的融合，显示了经典解决方案的全球存在。
This paper studies the non-negative solutions of the Keller-Segel model with a nonlocal nonlinear source in a bounded domain. The competition between the aggregation and the nonlocal reaction term is highlighted: when the growth factor is stronger than the dampening effect, with the help of the nonlocal term, the model admits a classical solution which is uniformly bounded. Moreover, when the growth factor is of the same order compared to the dampening effect, the nonlocal nonlinear exponents can prevent the chemotactic collapse. Global existence of classical solutions is shown for an appropriate range of the exponents as well as convergence to the constant equilibrium state.
