# 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-xing Gao and Anya Katsevich and Jianguo Liu and Jianfeng Lu and Jeremy Louis Marzuola}, journal={arXiv: Analysis of PDEs}, year={2020} }

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… Expand

#### 3 Citations

A Proximal-Gradient Algorithm for Crystal Surface Evolution

- Mathematics, Computer Science
- ArXiv
- 2020

This work develops a new numerical method based on the macroscopic partial differential equation, leveraging its formal structure as the gradient flow of the total variation energy, with respect to a weighted $H^{-1}$ norm, and proves convergence of the PDHG method to the semi-implicit scheme. Expand

From local equilibrium to numerical PDE: Metropolis crystal surface dynamics in the rough scaling limit

- Mathematics
- 2021

This paper builds off of recent work in which we studied the local equilibrium (LE) distribution of a microscopic crystal surface jump process with Arrhenius transition rates, under the so-called… Expand

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

- Mathematics
- 2021

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… Expand

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