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We analytically and numerically study a fourth order PDE modeling roughcrystal surface diffusion on the macroscopic level. We discuss existence ofsolutions globally in time and long time dynamics for the PDE model. The PDE,originally derived by the second author, is the continuum limit of amicroscopic model of the surface dynamics, given by a Markov jump process withMetropolis type transition rates. We outline the convergence argument, whichdepends on a simplifying assumption on the local equilibrium measure that isvalid in the high temperature regime. We provide numerical evidence for theconvergence of the microscopic model to the PDE in this regime.

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