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random diffusion

Proceedings of the Royal Society of Edinburgh Section A: Mathematics (1)

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1 results

The effects of diffusion on the principal eigenvalue for age-structured models with random diffusion
Part of
- Parabolic equations and systems
- General theory of linear operators
Hao Kang
Journal:

Proceedings of the Royal Society of Edinburgh. Section A: Mathematics / Volume 152 / Issue 1 / February 2022

Published online by Cambridge University Press:

23 March 2021, pp. 258-280

Print publication:

February 2022
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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.