A Diffuse-Interface Approach for Solid-State Dewetting with Anisotropic Surface Energies

Abstract We present a diffuse-interface model for the solid-state dewetting problem with anisotropic surface energies in $${\mathbb {R}}^d$$ R d $$d\in \{2,3\}$$ ∈ { 2 , 3 } . The introduced consists of Cahn–Hilliard equation, either smooth or double-obstacle potential, together degenerate mobility function and appropriate boundary conditions on wall. Upon regularizing model, help suitable asymptotic expansions, we recover as sharp-interface limit diffusion flow interface an Young’s law zero-flux condition at contact line fixed external boundary. Furthermore, show existence weak solutions regularized both obstacle potential. Numerical results based finite element approximation are presented to demonstrate excellent agreement between proposed its limit.