An Evolution System for a Class of Age-Structured Diffusive Population Equations

TL;DR

This paper applies Kato's theory to develop an evolution system for age-structured population equations with diffusion, establishing conditions for well-posedness of related quasilinear models.

Contribution

It introduces a novel application of Kato's theory to age-structured diffusive population equations, advancing the mathematical understanding of their well-posedness.

Findings

Established conditions for well-posedness of the quasilinear age-structured population model.

Extended Kato's theory to handle time-dependent diffusion in hyperbolic equations.

Provided a framework for analyzing age-structured population dynamics with diffusion.

Abstract

Kato's theory on the construction of strongly continuous evolution systems associated with hyperbolic equations is applied to the linear equation describing an age-structured population that is subject to time-dependent diffusion. The evolution system is used to provide conditions for the well-posedness of the corresponding quasilinear equation.