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On a non-linear size-structured population model

  • * Corresponding author: Yunfei Lv

    * Corresponding author: Yunfei Lv 

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

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  • 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.

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


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