2023/06/23 by Paolo Piovano, Piovano, Paolo, Francesco Sapio +1
Engineering · Materials Science · Mathematics · #Analysis of PDEs (math.AP) #Differential Equations and Numerical Methods #FOS: Mathematics #FOS: Physical sciences #Fluid Dynamics and Thin Films #Mathematical Physics (math-ph) #Solidification and crystal growth phenomena
paper · pdf · doi:10.48550/arxiv.2306.13432
openalex publication_date 2023/06/23 · openalex created_date 2023/06/27 · openalex updated_date 2026/07/28
The morphology of crystalline thin films evolving on flat rigid substrates by condensation of extra film atoms or by evaporation of their own atoms in the surrounding vapor is studied in the framework of the theory of Stress Driven Rearrangement Instabilities (SDRI). By following the literature both the elastic contributions due to the mismatch between the film and the substrate lattices at their theoretical (free-standing) elastic equilibrium, and a curvature perturbative regularization preventing the problem to be ill-posed due to the otherwise exhibited backward parabolicity, are added in the evolution equation. The resulting Cauchy problem under investigation consists in an anisotropic mean-curvature type flow of the fourth order on the film profiles, which are assumed to be parametrizable as graphs of functions measuring the film thicknesses, coupled with a quasistatic elastic problem in the film bulks. The existence of a regular solution for a finite period of time is established under periodic boundary conditions by means of employing minimizing movements to exploit the gradient-flow structure of the evolution equation.