Work

A Nonlocal Diffusion Single Population Model in Advective Environment

Year: 2025

Type: article

Abstract: ABSTRACT This paper is devoted to a nonlocal reaction–diffusion–advection model that describes the spatial dynamics of freshwater organisms in a river with a directional motion. Our goal is to investigate how the advection rate affects the dynamics of the species. We first establish the well‐posedness of global solutions, where the regularized problem containing a viscosity term and the re‐established maximum principle play key roles. We then demonstrate the existence, nonexistence, uniqueness, and stability of nontrivial stationary solutions by analyzing the principal eigenvalue of the integro‐differential operator, particularly focusing on its monotonicity with respect to the advection rate. This analysis helps us understand the long‐term dynamics of solutions and derive sharp criteria for persistence or extinction. Furthermore, we study the limiting behavior of solutions with respect to the advection rate and find that a sufficiently large advection rate leads to species extinction. Lastly, numerical simulations support our theoretical results.

Source: Mathematical Methods in the Applied Sciences

DOI: 10.1002/mma.10766

Authors: Yaobin Tang, Binxiang Dai

Institution: Central South University

Language: English

Topic: Mathematical and Theoretical Epidemiology and Ecology Models

Subfield: Public Health, Environmental and Occupational Health

Field: Medicine

Domain: Health Sciences

Open Access status: green

Funders: National Natural Science Foundation of China, Central South University, Fundamental Research Funds for the Central Universities, Fundamental Research Funds for Central Universities of the Central South University

Awards: G1793815134, G2752463960, 时滞反应扩散系统的分支问题与自由边界问题的理论和应用研究