2024/04/18 by Maurizio Grasselli, Grasselli, Maurizio, Luca Scarpa +3
Earth and Planetary Sciences · Materials Science · Physics and Astronomy · #35D30 #35K35 #35K86 #35Q92 #92C17 #Analysis of PDEs (math.AP) #FOS: Mathematics #Solidification and crystal growth phenomena #Theoretical and Computational Physics #nanoparticles nucleation surface interactions
paper · pdf · doi:10.48550/arxiv.2404.12113
openalex publication_date 2024/04/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
We consider local and nonlocal Cahn-Hilliard equations with constant mobility and singular potentials including, e.g., the Flory-Huggins potential, subject to no-flux (or periodic) boundary conditions. The main goal is to show that the presence of a suitable class of reaction terms allows to establish the existence of a weak solution to the corresponding initial and boundary value problem even though the initial condition is a pure state. In other words, the separation process takes place even in presence of a pure phase, provided that it is triggered by a convenient reaction term. This fact was already observed by the authors in a previous contribution devoted to a specific biological model. In this context, we generalize the previously-mentioned concept by examining the essential assumptions required for the reaction term to apply the new strategy. Also, we explore the scenario involving the nonlocal Cahn-Hilliard equation and provide illustrative examples that contextualize within our abstract framework.