Principal spectral theory and asymptotic behavior of the spectral bound for partially degenerate nonlocal dispersal systems

Autor: Zhang Lei
Jazyk: angličtina
Rok vydání: 2024
Předmět:
Zdroj: Advanced Nonlinear Studies, Vol 24, Iss 4, Pp 1012-1041 (2024)
Druh dokumentu: article
ISSN: 2169-0375
DOI: 10.1515/ans-2023-0148
Popis: The purpose of this paper is to investigate the principal spectral theory and asymptotic behavior of the spectral bound for cooperative nonlocal dispersal systems, specifically focusing on the case where partial diffusion coefficients are zero, referred to as the partially degenerate case. We propose two sufficient conditions that ensure the existence of the principal eigenvalue in these partially degenerate systems. Additionally, we study the asymptotic behavior of the spectral bound for nonlocal dispersal operators with small and large diffusion coefficients, considering both non-degenerate and partially degenerate cases. Notably, we find a threshold-type result as the diffusion coefficients tend towards infinity in the partially degenerate case. Finally, we apply these findings to discuss the asymptotic behavior of the basic reproduction ratio in a viral diffusion model.
Databáze: Directory of Open Access Journals