Analysis of a fourth-order exponential PDE arising from a crystal surface jump process with Metropolis-type transition rates

Abstract

We analytically and numerically study a fourth-order PDE modeling rough crystal surface diffusion on the macroscopic level. We discuss existence of solutions globally in time and long-time dynamics for the PDE model. The PDE, originally derived by Katsevich is the continuum limit of a microscopic model of the surface dynamics, given by a Markov jump process with Metropolis-type transition rates. We outline the convergence argument, which depends on a simplifying assumption on the local equilibrium measure that is valid in the high-temperature regime. We provide numerical evidence for the convergence of the microscopic model to the PDE in this regime.