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August  2020, 25(8): 3111-3133. doi: 10.3934/dcdsb.2020053

## On a non-linear size-structured population model

 1 School of Mathematical Sciences, Tiangong University, Tianjin, 300387, China 2 School of Mathematical Sciences, Beijing Normal University, Beijing, 100875, China

* Corresponding author: Yunfei Lv

Received  April 2019 Revised  October 2019 Published  February 2020

Fund Project: This research was partially supported by the National Natural Science Foundation of China (Nos. 11871371, 11971023, 11771044)

This paper deals with a size-structured population model consisting of a quasi-linear first-order partial differential equation with nonlinear boundary condition. The existence and uniqueness of solutions are firstly obtained by transforming the system into an equivalent integral equation such that the corresponding integral operator forms a contraction. Furthermore, the existence of global attractor is established by proving the asymptotic smoothness and eventual compactness of the nonlinear semigroup associated with the solutions. Finally, we discuss the uniform persistence and existence of compact attractor contained inside the uniformly persistent set.

Citation: Yunfei Lv, Yongzhen Pei, Rong Yuan. On a non-linear size-structured population model. Discrete & Continuous Dynamical Systems - B, 2020, 25 (8) : 3111-3133. doi: 10.3934/dcdsb.2020053
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