EXISTENCE THEOREMS FOR A FOURTH-ORDER EXPONENTIAL PDE RELATED TO CRYSTAL SURFACE RELAXATION

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. The equation we study was originally proposed to study the evolution of crystal surfaces, and was derived by applying a nonstandard scaling regime to a microscopic Markov jump process with Metropolis rates. Our investigation here finds that compared to the PDEs which use Arrhenius rates (and also have a fourth-order exponential nonlinearity), the hyperbolic sine nonlinearity in our equation can offer much better control over the exponent term even in high dimensions