Nonlinear age-structured population models with nonlocal diffusion and nonlocal boundary conditions

Hao Kang, Shigui Ruan

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

Abstract

In this paper, we develop some basic theory for age-structured population models with nonlocal diffusion and nonlocal boundary conditions. We first apply the theory of integrated semigroups and non-densely defined operators to a linear equation, study the spectrum, and analyze the asymptotic behavior via asynchronous exponential growth. Then we consider a semilinear equation with nonlocal diffusion and nonlocal boundary condition, use the method of characteristic lines to find the resolvent of the infinitesimal generator and the variation of constant formula, apply Krasnoselskii's fixed point theorem to obtain the existence of nontrivial steady states, and establish the stability of steady states. Finally we generalize these results to a nonlinear equation with nonlocal diffusion and nonlocal boundary condition.

Original languageEnglish (US)
Pages (from-to)430-462
Number of pages33
JournalJournal of Differential Equations
Volume278
DOIs
StatePublished - Mar 25 2021

Keywords

  • Age structure
  • Infinitesimal generator
  • Nonlocal diffusion
  • Semigroup theory
  • Spectrum theory
  • Stability

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

Fingerprint

Dive into the research topics of 'Nonlinear age-structured population models with nonlocal diffusion and nonlocal boundary conditions'. Together they form a unique fingerprint.

Cite this