-
Previous Article
Phase-field modelling of nonequilibrium partitioning during rapid solidification in a non-dilute binary alloy
- DCDS Home
- This Issue
-
Next Article
Introduction
A rapidly converging phase field model
1. | Department of Mathematics, University of Pittsburgh, Pittsburgh, PA 15260 |
2. | Institute of Applied Mathematics, University Erlangen-Nurenberg 91058 Erlangen |
[1] |
Leonid Berlyand, Mykhailo Potomkin, Volodymyr Rybalko. Sharp interface limit in a phase field model of cell motility. Networks and Heterogeneous Media, 2017, 12 (4) : 551-590. doi: 10.3934/nhm.2017023 |
[2] |
G. Caginalp, Christof Eck. Rapidly converging phase field models via second order asymptotics. Conference Publications, 2005, 2005 (Special) : 142-152. doi: 10.3934/proc.2005.2005.142 |
[3] |
Antonio DeSimone, Martin Kružík. Domain patterns and hysteresis in phase-transforming solids: Analysis and numerical simulations of a sharp interface dissipative model via phase-field approximation. Networks and Heterogeneous Media, 2013, 8 (2) : 481-499. doi: 10.3934/nhm.2013.8.481 |
[4] |
Helmut Abels, Johannes Kampmann. Existence of weak solutions for a sharp interface model for phase separation on biological membranes. Discrete and Continuous Dynamical Systems - S, 2021, 14 (1) : 331-351. doi: 10.3934/dcdss.2020325 |
[5] |
Liupeng Wang, Yunqing Huang. Error estimates for second-order SAV finite element method to phase field crystal model. Electronic Research Archive, 2021, 29 (1) : 1735-1752. doi: 10.3934/era.2020089 |
[6] |
Matthieu Alfaro, Arnaud Ducrot. Sharp interface limit of the Fisher-KPP equation. Communications on Pure and Applied Analysis, 2012, 11 (1) : 1-18. doi: 10.3934/cpaa.2012.11.1 |
[7] |
Shi Jin, Min Tang, Houde Han. A uniformly second order numerical method for the one-dimensional discrete-ordinate transport equation and its diffusion limit with interface. Networks and Heterogeneous Media, 2009, 4 (1) : 35-65. doi: 10.3934/nhm.2009.4.35 |
[8] |
Honghu Liu. Phase transitions of a phase field model. Discrete and Continuous Dynamical Systems - B, 2011, 16 (3) : 883-894. doi: 10.3934/dcdsb.2011.16.883 |
[9] |
Pierre-Étienne Druet. Some mathematical problems related to the second order optimal shape of a crystallisation interface. Discrete and Continuous Dynamical Systems, 2015, 35 (6) : 2443-2463. doi: 10.3934/dcds.2015.35.2443 |
[10] |
Takayuki Kubo, Yoshihiro Shibata, Kohei Soga. On some two phase problem for compressible and compressible viscous fluid flow separated by sharp interface. Discrete and Continuous Dynamical Systems, 2016, 36 (7) : 3741-3774. doi: 10.3934/dcds.2016.36.3741 |
[11] |
Matthieu Alfaro, Arnaud Ducrot. Sharp interface limit of the Fisher-KPP equation when initial data have slow exponential decay. Discrete and Continuous Dynamical Systems - B, 2011, 16 (1) : 15-29. doi: 10.3934/dcdsb.2011.16.15 |
[12] |
Dohyun Kim. Asymptotic behavior of a second-order swarm sphere model and its kinetic limit. Kinetic and Related Models, 2020, 13 (2) : 401-434. doi: 10.3934/krm.2020014 |
[13] |
Kai Jiang, Wei Si. High-order energy stable schemes of incommensurate phase-field crystal model. Electronic Research Archive, 2020, 28 (2) : 1077-1093. doi: 10.3934/era.2020059 |
[14] |
G. Caginalp, Emre Esenturk. Anisotropic phase field equations of arbitrary order. Discrete and Continuous Dynamical Systems - S, 2011, 4 (2) : 311-350. doi: 10.3934/dcdss.2011.4.311 |
[15] |
John M. Ball, Carlos Mora-Corral. A variational model allowing both smooth and sharp phase boundaries in solids. Communications on Pure and Applied Analysis, 2009, 8 (1) : 55-81. doi: 10.3934/cpaa.2009.8.55 |
[16] |
Pierluigi Colli, Gianni Gilardi, Pavel Krejčí, Jürgen Sprekels. A vanishing diffusion limit in a nonstandard system of phase field equations. Evolution Equations and Control Theory, 2014, 3 (2) : 257-275. doi: 10.3934/eect.2014.3.257 |
[17] |
Michael Grinfeld, Amy Novick-Cohen. Some remarks on stability for a phase field model with memory. Discrete and Continuous Dynamical Systems, 2006, 15 (4) : 1089-1117. doi: 10.3934/dcds.2006.15.1089 |
[18] |
A. Jiménez-Casas. Invariant regions and global existence for a phase field model. Discrete and Continuous Dynamical Systems - S, 2008, 1 (2) : 273-281. doi: 10.3934/dcdss.2008.1.273 |
[19] |
Alberto Bressan, Marco Mazzola, Hongxu Wei. A dynamic model of the limit order book. Discrete and Continuous Dynamical Systems - B, 2020, 25 (3) : 1015-1041. doi: 10.3934/dcdsb.2019206 |
[20] |
Seung-Yeal Ha, Jinwook Jung, Jeongho Kim, Jinyeong Park, Xiongtao Zhang. A mean-field limit of the particle swarmalator model. Kinetic and Related Models, 2021, 14 (3) : 429-468. doi: 10.3934/krm.2021011 |
2021 Impact Factor: 1.588
Tools
Metrics
Other articles
by authors
[Back to Top]