2021/04/26 by Bruna C. dos Santos, Santos, Bruna C. dos, Sergio Oliva +3
Computer Science · Mathematics · #35A05 #35B40 #35K55 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Differential Equations and Boundary Problems #Differential Equations and Numerical Methods #FOS: Mathematics
paper · pdf · doi:10.48550/arxiv.2104.12833
openalex publication_date 2021/04/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
In this paper, we analyze a model composed by coupled local and nonlocal diffusion equations acting in different subdomains. We consider the limit case when one of the subdomains is thin in one direction (it is concentrated to a domain of smaller dimension) and as a limit problem we obtain coupling between local and nonlocal equations acting in domains of different dimension. We find existence and uniqueness of solutions and we prove several qualitative properties (like conservation of mass and convergence to the mean value of the initial condition as time goes to infinity).