2025/02/06 by Sheetal Dharmatti, Dharmatti, Sheetal, K Greeshma +1
Mathematics · Medicine · #35B40 #35B45 #35K55 #76D99 #76S05 #76T99 #Analysis of PDEs (math.AP) #Differential Equations and Boundary Problems #Differential Equations and Numerical Methods #FOS: Mathematics #Mathematical and Theoretical Epidemiology and Ecology Models
paper · pdf · doi:10.48550/arxiv.2502.04222
openalex publication_date 2025/02/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This work studies the nonlocal Cahn Hilliard Brinkman system, which models the phase separation of a binary fluid in a bounded domain and porous media. We focus on a system with a singular potential namely logarithmic form and a degenerate mobility function. The singular potential introduces challenges due to the blow up of its derivatives near pure phases, while the degenerate mobility complicates the analysis. Our main result is the separation property, which ensures that the solution eventually stays away from the pure phases. We adopt a new method, inspired by the De Giorgi iteration, introduced for the two dimensional Cahn Hilliard equation with constant mobility. This work extends previous results and provides a general approach for proving the separation property for similar systems.