Asymptotic properties of the inhomogeneous Lotka‐Von Foerster system

In this paper, we investigate an extension of the multistate stable population model, which makes allowances for migration. The model is formulated as an inhomogeneous system of first order partial differential equations with integral boundary conditions. First, we construct its classical solution. Next, we reformulate the system as an abstract inhomogeneous Cauchy problem on a Banach space, and give its mild solution by using the population semigroup. Our main purpose is to investigate the asymptotic behavior of the mild solution.

Key words:

• Lotka‐Von Foerster system
• Cauchy problem
• population semigroup
• multistate population
• asymptotic properties
• inhomogeneity