Global Existence of a Strong Solution to a Fourth-Order Exponential PDE Modelling Crystal Surface Growth With Metropolis-Type Rates

Abstract

In this article we prove the global existence of a unique strong solution to the initial boundary-value problem for a fourth-order exponential PDE modeling crystal surface growth. The model we study is derived as the limit of a microscopic Markov jump process with Metropolis-type transition rates. Our investigation reveals that, in opposition to the models with Arrhenius rates, where the exponent may contain a singular part, the exponent in our model is a W 1,2 function.