Existence and uniqueness of solutions for a hierarchical system of two age-structured populations

Abstract

We propose a class of new hierarchical model for the evolution of two interacting age-structured populations, which is a system of integro-partial differential equations with global feedback boundary conditions and may describe the interactions such as competition, cooperation and predator-prey relation. Based upon a group of natural conditions, the existence and uniqueness of solutions on infinite time interval are proved by means of fixed point and extension principle, and the continuous dependence of the solution on the initial age distribution is established. These results lay a sound basis for the investigation of stability, controllability and variable optimal control problems.

Key words： Hierarchy of ages; population system; integro-partial differential equations; existence and uniqueness; fixed points

Acknowledgements

This work was supported by the National Natural Science Foundation of China (Grant No. 11871185) and the Natural Science Foundation of Zhejiang Province (No. LY18A010010).

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