Work

Propagation dynamics of a free boundary problem with advection and preferred density

Year: 2026

Type: article

Abstract: This paper mainly studies a reaction-diffusion-advection free boundary problem with a preferred density boundary condition, which models the spatial spread of a species. The species tends to maintain a specific density δ > 0 at the spreading fronts, and this condition significantly affects the invasion dynamics. We establish the well-posedness of the solution and rigorously prove a trichotomy for population evolution: spreading occurs when 0 < δ < 1 , transition occurs when δ = 1 , and vanishing happens when δ > 1 . The method used for the case δ = 1 also resolves Conjecture 4 in [19] in the symmetric version. In the spreading case, we precisely obtain for the first time the asymptotic speeds of the left and right spreading fronts and their dependence on the advection strength β . Moreover, we reveal a structural transition in the left propagation pattern from a semi-wave to a traveling wave when β exceeds a threshold β ⁎ . This study systematically elucidates the coupling influence of the preferred density and advection effects on biological invasion dynamics.

Source: Journal of Differential Equations

DOI: 10.1016/j.jde.2026.114602

Authors: Hongkai Cao, Cuiming Ma, Xiaoyan Zhang

Institution: Shandong 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: hybrid

Estimated APC paid: $3,550

Funders: National Natural Science Foundation of China, Natural Science Foundation of Shandong Province