Mathematical analysis of autonomous and non‐autonomous age‐structured reaction‐diffusion‐advection population model

Abstract

In this paper, we study an age-structured reaction-diffusion-advection population model. First, we use a non-densely defined operator to the linear age-structured reaction-diffusion-advection population model in a patchy environment. By spectral analysis, we obtain the asynchronous exponential growth of the population model. Then we consider nonlinear death rate and birth rate, which all depend on the function related to the generalized total population, and we prove the existence of a steady state of the system. Finally, we study the age-structured reaction-diffusion-advection population model in non-autonomous situations. We give the comparison principle and prove the eventual compactness of semiflow by using integrated semigroup. We also prove the existence of compact attractors under the periodic situation.

Dynamics and asymptotic profiles on an age-structured SIS epidemic model with random diffusion and advection

“…where the first and third equations, the final equation, and the second inequality hold due to (43), (16), and (17), respectively. Note that there exists a small constant c > 0 such that e − 1 α (a−σ) ≥ c. So we have…”

“…Following the early studies of [39,40], many hyperbolic-parabolic partial differential equations are applied to describe age-structured models with spatial diffusion. For more results of several age-structured models, refer to [33,29,32,16,12,10,11].…”