两物种抛物-抛物排斥趋化模型解的渐进行为

Asymptotic Behavior of Solutions to a Parabolic-Parabolic Repulsion Chemotaxis Model with Two Species

两物种抛物-抛物排斥趋化模型描述了两不同物种对同一种化学物质产生趋化排斥作用.对于充分光滑的初始数据,利用压缩不动点定理和先验估计技巧,证明了该模型存在唯一且有界的整体光滑解,并利用Lyapunov泛函证明了该整体解指数收敛到常数稳态解.

A parabolic-parabolic repulsion chemotaxis model with two species considers two different species interacting with repulsive signaling chemicals. By the fixed-point argument and a priori estimate technique, the first result can be stated that the model admits a unique global smooth solution which is uniformly-in-time bounded, provided initial data is smooth. Moreover, based on a Lyapunov functional, the second result is established that this solution converges to a stationary solution as time goes to infinity.