Analysis of a fourth-order exponential PDE arising from a crystal surface jump process with Metropolis-type transition rates
| Autor: | Yuan Gao, Anya E. Katsevich, Jian-Guo Liu, Jianfeng Lu, Jeremy L. Marzuola |
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| Rok vydání: | 2021 |
| Předmět: | |
| Zdroj: | Pure and Applied Analysis. 3:595-612 |
| ISSN: | 2578-5885 2578-5893 |
| DOI: | 10.2140/paa.2021.3.595 |
| Popis: | 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. 14 pages, 4 figures, comments welcome! Revised significantly thanks to very thorough referee reports. Some previous discussions have been removed and will be reported in a separate result by one of the authors |
| Databáze: | OpenAIRE |
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