• DOI:10.2140/paa.2021.3.595
• Corpus ID: 212725293

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

@article{Gao2020AnalysisOA,
  title={Analysis of a fourth-order exponential PDE arising from a crystal surface jump process with Metropolis-type transition rates},
  author={Yuan Gao and Anya Katsevich and Jian‐Guo Liu and Jianfeng Lu and Jeremy Louis Marzuola},
  journal={Pure and Applied Analysis},
  year={2020}
}

• Yuan Gao, A. Katsevich, +2 authors J. Marzuola
• Published 16 March 2020
• Mathematics
• Pure and Applied Analysis

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 the second author, 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.