Work

The anisotropic Cahn–Hilliard equation with degenerate mobility: Existence of weak solutions

Year: 2025

Type: article

Abstract: This paper presents an existence result for the anisotropic Cahn–Hilliard equation characterized by a potentially concentration-dependent degenerate mobility taking into account an anisotropic energy. The model allows for the degeneracy of the mobility at specific concentration values, demonstrating that the solution remains within physically relevant bounds. The introduction of anisotropy leads to highly nonlinear terms making energy and entropy estimates rather involved. As the mobility degenerates in the pure phases, the degenerate Cahn–Hilliard equation describes surface diffusion and is an important model to model solid-state dewetting (SSD) of thin films. We show existence of weak solutions for the anisotropic degenerate Cahn–Hilliard equation by using suitable energy- and entropy-type estimates.

Source: Analysis and Applications

DOI: 10.1142/s0219530526500144

Authors: Harald Garcke, Patrik Knopf, Andrea Signori

Institutions: University of Regensburg, Politecnico di Milano

Language: English

Topic: Solidification and crystal growth phenomena

Subfield: Materials Chemistry

Field: Materials Science

Domain: Physical Sciences

Open Access status: green

Funder: Deutsche Forschungsgemeinschaft

Award: G3270504644