Connecting the Deep Quench Obstacle Problem with Surface Diffusion via Their Steady States

Eric A. Carlen; Amy Novick-Cohen; Lydia Peres Hari

doi:10.1007/978-3-031-65195-3_11

Connecting the Deep Quench Obstacle Problem with Surface Diffusion via Their Steady States

Eric A. Carlen, Amy Novick-Cohen, Lydia Peres Hari

Mathematics

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

Abstract

In modeling phase transitions, it is useful to be able to connect diffuse interface descriptions of the dynamics with corresponding limiting sharp interface motions. In the case of the deep quench obstacle problem (DQOP) and surface diffusion (SD), while a formal connection was demonstrated many years ago, rigorous proof of the connection has yet to be established. In the present note, we show how information regarding the steady states for both these motions can provide insight into the dynamic connection, and we outline tools that should enable further progress. For simplicity, we take both motions to be defined on a planar disk.

Original language	English
Title of host publication	From Particle Systems to Partial Differential Equations - PSPDE X 2022
Editors	Eric Carlen, Patrícia Gonçalves, Ana Jacinta Soares
Pages	239-267
Number of pages	29
DOIs	https://doi.org/10.1007/978-3-031-65195-3_11
State	Published - 2024
Event	10th International Conference on Particle Systems and Partial Differential Equations, PSPDE 2022 - Braga, Portugal Duration: 26 Jun 2022 → 30 Jun 2022

Publication series

Name	Springer Proceedings in Mathematics and Statistics
Volume	465
ISSN (Print)	2194-1009
ISSN (Electronic)	2194-1017

Conference

Conference	10th International Conference on Particle Systems and Partial Differential Equations, PSPDE 2022
Country/Territory	Portugal
City	Braga
Period	26/06/22 → 30/06/22

Keywords

Deep quench obstacle problem
Geometric motions
Higher order degenerate parabolic equations
Limiting motions
Surface diffusion

ASJC Scopus subject areas

General Mathematics

Access to Document

10.1007/978-3-031-65195-3_11

Cite this

Carlen, E. A., Novick-Cohen, A., & Hari, L. P. (2024). Connecting the Deep Quench Obstacle Problem with Surface Diffusion via Their Steady States. In E. Carlen, P. Gonçalves, & A. J. Soares (Eds.), From Particle Systems to Partial Differential Equations - PSPDE X 2022 (pp. 239-267). (Springer Proceedings in Mathematics and Statistics; Vol. 465). https://doi.org/10.1007/978-3-031-65195-3_11

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Carlen, EA, Novick-Cohen, A & Hari, LP 2024, Connecting the Deep Quench Obstacle Problem with Surface Diffusion via Their Steady States. in E Carlen, P Gonçalves & AJ Soares (eds), From Particle Systems to Partial Differential Equations - PSPDE X 2022. Springer Proceedings in Mathematics and Statistics, vol. 465, pp. 239-267, 10th International Conference on Particle Systems and Partial Differential Equations, PSPDE 2022, Braga, Portugal, 26/06/22. https://doi.org/10.1007/978-3-031-65195-3_11

Connecting the Deep Quench Obstacle Problem with Surface Diffusion via Their Steady States. / Carlen, Eric A.; Novick-Cohen, Amy; Hari, Lydia Peres.
From Particle Systems to Partial Differential Equations - PSPDE X 2022. ed. / Eric Carlen; Patrícia Gonçalves; Ana Jacinta Soares. 2024. p. 239-267 (Springer Proceedings in Mathematics and Statistics; Vol. 465).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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