Local minimizers and slow motion for the mass preserving Allen–Cahn equation in higher dimensions
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- by Giovanni Leoni and Ryan Murray PDF
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Abstract:
This paper completely resolves the asymptotic development of order $2$ by $\Gamma$-convergence of the mass-constrained Cahn–Hilliard functional. Important new results on the slow motion of interfaces for the mass preserving Allen–Cahn equation and the Cahn–Hilliard equations in higher dimension are obtained as an application.References
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Additional Information
- Giovanni Leoni
- Affiliation: Department of Mathematical Sciences, Carnegie Mellon University, Pittsburgh, Pennsylvania 15213
- MR Author ID: 321623
- Ryan Murray
- Affiliation: Department of Mathematics, North Carolina State University, Raleigh, North Carolina 27695
- MR Author ID: 132207
- Received by editor(s): July 15, 2017
- Received by editor(s) in revised form: October 14, 2017
- Published electronically: September 23, 2019
- Additional Notes: The authors warmly thank the Center for Nonlinear Analysis, where part of this work was carried out. The center is partially supported by NSF Grant No. DMS-0635983 and NSF PIRE Grant No. OISE-0967140.
The research of the first author was partially funded by the NSF under Grants No. DMS-1412095 and DMS-1714098.
The research of the second author was supported by NSF PIRE Grant No. OISE-0967140. - Communicated by: Joachim Krieger
- © Copyright 2019 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 147 (2019), 5167-5182
- MSC (2010): Primary 49J45, 35K10, 35K25
- DOI: https://doi.org/10.1090/proc/13988
- MathSciNet review: 4021078