American Institute of Mathematical Sciences

Advanced
February  2004, 10(1&2): 239-252. doi: 10.3934/dcds.2004.10.239

Long-time behaviour and convergence towards equilibria for a conserved phase field model

Eduard Feireisl 1, , Françoise Issard-Roch 2, and  Hana Petzeltová 3,

1. 

Institute of Mathematics AS ČR, Žitná 25, 115 67 Praha 1, Czech Republic
2. 

Laboratoire de Mathématique, Analyse Numérique et E.D.P., Bâtiment 425, Université de Paris Sud, 91405 Orsay cedex, France
3. 

Mathematical Institute AV ČR, Žitná 25, 115 67 Praha 1, Czech Republic

Received  June 2001 Revised  October 2002 Published  October 2003

We prove convergence towards an equilibrium state for any globally defined solution for a conserved phase field model. A generalized version of the Lojasiewicz-Simon theorem is used.
Keywords: Lojasiewicz theorem., Conserved phase field model, convergence.
Mathematics Subject Classification: 35B40, 80A2.
Citation: Eduard Feireisl, Françoise Issard-Roch, Hana Petzeltová. Long-time behaviour and convergence towards equilibria for a conserved phase field model. Discrete & Continuous Dynamical Systems, 2004, 10 (1&2) : 239-252. doi: 10.3934/dcds.2004.10.239
[1]

Sergiu Aizicovici, Hana Petzeltová. Convergence to equilibria of solutions to a conserved Phase-Field system with memory. Discrete & Continuous Dynamical Systems - S, 2009, 2 (1) : 1-16. doi: 10.3934/dcdss.2009.2.1
[2]

Pavel Krejčí, Songmu Zheng. Pointwise asymptotic convergence of solutions for a phase separation model. Discrete & Continuous Dynamical Systems, 2006, 16 (1) : 1-18. doi: 10.3934/dcds.2006.16.1
[3]

Federico Mario Vegni. Dissipativity of a conserved phase-field system with memory. Discrete & Continuous Dynamical Systems, 2003, 9 (4) : 949-968. doi: 10.3934/dcds.2003.9.949
[4]

Ahmed Bonfoh, Cyril D. Enyi. Large time behavior of a conserved phase-field system. Communications on Pure & Applied Analysis, 2016, 15 (4) : 1077-1105. doi: 10.3934/cpaa.2016.15.1077
[5]

Pierluigi Colli, Gianni Gilardi, Gabriela Marinoschi, Elisabetta Rocca. Optimal control for a conserved phase field system with a possibly singular potential. Evolution Equations & Control Theory, 2018, 7 (1) : 95-116. doi: 10.3934/eect.2018006
[6]

Jacek Banasiak, Amartya Goswami. Singularly perturbed population models with reducible migration matrix 1. Sova-Kurtz theorem and the convergence to the aggregated model. Discrete & Continuous Dynamical Systems, 2015, 35 (2) : 617-635. doi: 10.3934/dcds.2015.35.617
[7]

Theodore Tachim Medjo. On the convergence of a stochastic 3D globally modified two-phase flow model. Discrete & Continuous Dynamical Systems, 2019, 39 (1) : 395-430. doi: 10.3934/dcds.2019016
[8]

Pierluigi Colli, Gianni Gilardi, Philippe Laurençot, Amy Novick-Cohen. Uniqueness and long-time behavior for the conserved phase-field system with memory. Discrete & Continuous Dynamical Systems, 1999, 5 (2) : 375-390. doi: 10.3934/dcds.1999.5.375
[9]

Alain Miranville. Asymptotic behavior of the conserved Caginalp phase-field system based on the Maxwell-Cattaneo law. Communications on Pure & Applied Analysis, 2014, 13 (5) : 1971-1987. doi: 10.3934/cpaa.2014.13.1971
[10]

Gianluca Mola. Global attractors for a three-dimensional conserved phase-field system with memory. Communications on Pure & Applied Analysis, 2008, 7 (2) : 317-353. doi: 10.3934/cpaa.2008.7.317
[11]

Ahmed Bonfoh, Ibrahim A. Suleman. Robust exponential attractors for singularly perturbed conserved phase-field systems with no growth assumption on the nonlinear term. Communications on Pure & Applied Analysis, 2021, 20 (10) : 3639-3666. doi: 10.3934/cpaa.2021125
[12]

Honghu Liu. Phase transitions of a phase field model. Discrete & Continuous Dynamical Systems - B, 2011, 16 (3) : 883-894. doi: 10.3934/dcdsb.2011.16.883
[13]

Haiyan Yin, Changjiang Zhu. Convergence rate of solutions toward stationary solutions to a viscous liquid-gas two-phase flow model in a half line. Communications on Pure & Applied Analysis, 2015, 14 (5) : 2021-2042. doi: 10.3934/cpaa.2015.14.2021
[14]

Yukie Goto, Danielle Hilhorst, Ehud Meron, Roger Temam. Existence theorem for a model of dryland vegetation. Discrete & Continuous Dynamical Systems - B, 2011, 16 (1) : 197-224. doi: 10.3934/dcdsb.2011.16.197
[15]

Ciprian G. Gal. Robust exponential attractors for a conserved Cahn-Hilliard model with singularly perturbed boundary conditions. Communications on Pure & Applied Analysis, 2008, 7 (4) : 819-836. doi: 10.3934/cpaa.2008.7.819
[16]

Pierluigi Colli, Danielle Hilhorst, Françoise Issard-Roch, Giulio Schimperna. Long time convergence for a class of variational phase-field models. Discrete & Continuous Dynamical Systems, 2009, 25 (1) : 63-81. doi: 10.3934/dcds.2009.25.63
[17]

M. Grasselli, Hana Petzeltová, Giulio Schimperna. Convergence to stationary solutions for a parabolic-hyperbolic phase-field system. Communications on Pure & Applied Analysis, 2006, 5 (4) : 827-838. doi: 10.3934/cpaa.2006.5.827
[18]

Stig-Olof Londen, Hana Petzeltová. Convergence of solutions of a non-local phase-field system. Discrete & Continuous Dynamical Systems - S, 2011, 4 (3) : 653-670. doi: 10.3934/dcdss.2011.4.653
[19]

Shaoqiang Tang, Huijiang Zhao. Stability of Suliciu model for phase transitions. Communications on Pure & Applied Analysis, 2004, 3 (4) : 545-556. doi: 10.3934/cpaa.2004.3.545
[20]

Xinfu Chen, G. Caginalp, Christof Eck. A rapidly converging phase field model. Discrete & Continuous Dynamical Systems, 2006, 15 (4) : 1017-1034. doi: 10.3934/dcds.2006.15.1017

2020 Impact Factor: 1.392

Tools

Metrics

  • PDF downloads (60)
  • HTML views (0)
  • Cited by (1)

Other articles
by authors

[Back to Top]

Copyright © 2021 American Institute of Mathematical Sciences