Degenerate Cahn–Hilliard systems: From nonlocal to local
José A. Carrillo, Charles Elbar, Jakub Skrzeczkowski
Abstract
We provide a rigorous mathematical framework to establish the limit of a nonlocal model of cell–cell adhesion system to a local model. When the parameter of the nonlocality goes to 0, the system tends to a Cahn–Hilliard system with degenerate mobility and cross-interaction forces. Our analysis relies on a-priori estimates and compactness properties.
Topics & Concepts
MathematicsDegenerate energy levelsCahn–Hilliard equationMathematical analysisPhysicsQuantum mechanicsPartial differential equationSolidification and crystal growth phenomena