2018/12/17 by Xiaoming Fu, Fu, Xiaoming, Pierre Magal +1 · 1 citation
Computer Science · Mathematics · Medicine · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Mathematical Biology Tumor Growth #Mathematical and Theoretical Epidemiology and Ecology Models
paper · pdf · doi:10.48550/arxiv.1812.06733
openalex publication_date 2018/12/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we consider a nonlocal advection model for two populations on a bounded domain. The first part of the paper is devoted to the existence and uniqueness of solutions and the associated semi-flow properties. Here we use the notion of solution integrated along the characteristics. Next, by proving segregation property, we construct an energy functional to investigate the asymptotic behavior of the solution. In order to get some compactness of the positive orbit, we use the narrow convergence in the space of Young measures. By using this idea, we get a description of the asymptotic behavior of the solution in the space of Young measures. The last section of the paper is devoted to numerical simulations, which confirm and complement our theoretical results.