On a non-linear size-structured population model

Yunfei Lv; Yongzhen Pei; Rong Yuan

doi:10.3934/dcdsb.2020053

Article Contents

2020, Volume 25, Issue 8: 3111-3133. Doi: 10.3934/dcdsb.2020053

This issue Previous Article Long-term orbit dynamics viewed through the yellow main component in the parameter space of a family of optimal fourth-order multiple-root finders Next Article Attractors for a class of delayed reaction-diffusion equations with dynamic boundary conditions

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
^* Corresponding author: Yunfei Lv

Received: April 2019

Revised: October 2019

Early access: February 2020

Published: August 2020

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

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Abstract

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.

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Mathematics Subject Classification: Primary: 35Q92, 35L03, 35B41; Secondary: 92D25.

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