This paper investigates the diffusive logistic equation with a sedentary compartment and free boundary whose dynamics has been considered by Wang and Cao (2015) when the intrinsic rate of reproduction in the stationary class is less than the rate of switching from stationary to mobile. However, the case is left as an open problem in Wang and Cao (2015). We shall show that spreading happens if and give the longtime behavior.

中文翻译：

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具有固定隔间和自由边界的扩散 Logistic 方程的动力学

本文研究了具有固定隔间和自由边界的扩散逻辑方程，当固定类别的内在繁殖率小于从固定类别切换到移动类别的速率时，Wang 和 Cao (2015) 考虑了该方程的动力学。然而，该案在 Wang 和 Cao (2015) 中仍然是一个悬而未决的问题。我们将证明，如果 并给出长期行为，就会发生传播。