Approximation of random diffusion by nonlocal diffusion in age-structured models

Hao Kang, Shigui Ruan

Research output: Contribution to journalArticlepeer-review

Abstract

In this paper we study the approximation of random diffusion by nonlocal diffusion with properly rescaled kernels in age-structured models. First we show that solutions of age-structured models with nonlocal diffusion under Dirichlet and Neumann boundary conditions converge to solutions of the corresponding age-structured models with random diffusion under Dirichlet and Neumann boundary conditions, respectively. Then we prove that the principal eigenvalues of the nonlocal operators in age-structured models under Dirichlet and Neumann boundary conditions converge to the principal eigenvalues of the corresponding Laplace operators in age-structured models under Dirichlet and Neumann boundary conditions, respectively.

Original languageEnglish (US)
Article number108
JournalZeitschrift fur Angewandte Mathematik und Physik
Volume72
Issue number3
DOIs
StatePublished - Jun 2021

Keywords

  • Age structure
  • Approximation
  • Nonlocal/random diffusion
  • Positive solutions
  • Principal eigenvalue

ASJC Scopus subject areas

  • Mathematics(all)
  • Physics and Astronomy(all)
  • Applied Mathematics

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