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Analysis of a
fourth-order exponential PDE arising from a crystal surface
jump process with Metropolis-type transition rates
Yuan Gao, Anya E. Katsevich, Jian-Guo Liu, Jianfeng Lu and Jeremy L. Marzuola |
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Vol. 3 (2021), No. 4, 595–612
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Abstract |
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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 Katsevich 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. |
Keywords
crystal surface relaxation, gradient flows, metropolis
rates
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Mathematical Subject Classification 2010
Primary: 35Q70, 82D25
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Milestones
Received: 16 March 2020
Revised: 19 November 2020
Accepted: 29 April 2021
Published: 12 February 2022
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Authors |
| Yuan Gao | |
| Department of Mathematics Purdue University West Lafayette, IN United States |
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| Anya E. Katsevich | |
| Courant Institute of Mathematical
Sciences New York University New York City, NY United States |
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| Jian-Guo Liu | |
| Departments of Mathematics and
Physics Duke University Durham, NC United States |
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| Jianfeng Lu | |
| Departments of Mathematics, Physics
and Chemistry Duke University Durham, NC United States |
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| Jeremy L. Marzuola | |
| Department of Mathematics University of North Carolina Chapel Hill, NC United States |
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