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The effects of diffusion on the principal eigenvalue for age-structured models with random diffusion

Part of: General theory of linear operators Parabolic equations and systems

Published online by Cambridge University Press:  23 March 2021

Hao Kang
Hao Kang*
Affiliation:
Department of Mathematics, University of Miami, Coral Gables, FL 33146, USA (haokang@math.miami.edu)
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Abstract

In this paper, we study the principal spectral theory of age-structured models with random diffusion. First, we provide an equivalent characteristic for the principal eigenvalue, the strong maximum principle and a positive strict super-solution. Then, we use the result to investigate the effects of diffusion rate on the principal eigenvalue. Finally, we study how the principal eigenvalue affects the global dynamics of the KPP model and verify that the principal eigenvalue being zero is a critical value.

Keywords

Age structureglobal dynamicsprincipal eigenvaluerandom diffusionstrong maximum principle

MSC classification

Primary: 35K57: Reaction-diffusion equations
Secondary: 92D25: Population dynamics (general) 47A10: Spectrum, resolvent
Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 152 , Issue 1 , February 2022 , pp. 258 - 280
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Copyright
Copyright © The Author(s), 2021. Published by Cambridge University Press on behalf of The Royal Society of Edinburgh

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