一个在抑素作用下logistic生长模型的定性研究

A QUALITATIVE STUDY OF A MODEL DESCRIBING LOGISTIC GROWTH UNDER THE INHIBITION OF CHALONES

研究了在抑制因素作用下含扩散的logistic生长模型的波解问题。运用Lia-pounov函数法分析了均匀定态的稳定性;通过比较方法及不变矩形论证了解的全局稳定性,证明初值解具有无限多个不变矩形;讨论了波解的存在性并运用强极大原理及非负性论证研究了波速。

The initial value problem of a model describing the logistic tissue growth inhibited by chalones is studied. By using the Liapounov function it is concluded that the steady state P_1=(1,1) is asymototiclly stable. By using the comparison method, the global existence of the solution of an initial value problem is examined and it is found that the solution admits infinitely many invariant rectangles. Finally, the existence and the monotonicity problem of the wave front solution is studied and the asympototically stable wave speed is provided by applying the strong maximum principle and the nonnegative argument.