带Logistic源的抛物-椭圆趋化模型解的大时间行为

摘要

A parabolic-elliptic chemotaxis model with generalized logistic source is considered in this paper. First, based on a fixed point argument, Lp-estimate technique and Moser's iteration, it is proved that the model has a globally-in-time bounded solution under the assumption that the coefficient of logistic dampening is positive. Then, under the assumptions the coefficient of logistic dampening is sufficiently large and the initial cell density has a positive lower bound, it is shown that the solution converges to a non-zero stationary solution exponentially in L2(Ω) as t→+ ∞ by up and sub-solution method and energy estimate technique.%考虑带logistic源的抛物-椭圆趋化模型.用不动点原理,Lp估计技巧和Moser迭代证明了对任意的正的logistic阻尼系数,该模型整体解存在且一致有界.当logistic阻尼系数充分大和在初值有正下界的假设之下,通过构造上、下解和能量估计,证明了解在L2(Ω)空间中指数收敛到非零常数稳态.