American Institute of Mathematical Sciences

Advanced
September  2006, 6(5): 1001-1026. doi: 10.3934/dcdsb.2006.6.1001

Modelling and long-time behaviour for phase transitions with entropy balance and thermal memory conductivity

Elena Bonetti 1, , Pierluigi Colli 1, , Mauro Fabrizio 2, and  Gianni Gilardi 1,

1. 

Dipartimento di Matematica "F. Casorati", Università di Pavia, Via Ferrata 1, 27100 Pavia, Italy, Italy
2. 

Dipartimento di Matematica, Università di Bologna, Piazza di Porta San Donato 5, 40126 Bologna, Italy

Received  September 2005 Revised  November 2005 Published  June 2006

This paper deals with a thermomechanical model describing phase transitions with thermal memory in terms of balance and equilibrium equations for entropy and microforces, respectively. After a presentation and discussion of the model, the large time behaviour of the solutions to the related integro-differential system of PDE's is investigated.
Keywords: long-time behaviour of solutions., microforces, thermal memory, entropy, Phase transition model, non-linear initial-boundary value problem.
Mathematics Subject Classification: Primary: 35K60, 35Q99, 80A2.
Citation: Elena Bonetti, Pierluigi Colli, Mauro Fabrizio, Gianni Gilardi. Modelling and long-time behaviour for phase transitions with entropy balance and thermal memory conductivity. Discrete & Continuous Dynamical Systems - B, 2006, 6 (5) : 1001-1026. doi: 10.3934/dcdsb.2006.6.1001
[1]

Ke Xu, M. Gregory Forest, Xiaofeng Yang. Shearing the I-N phase transition of liquid crystalline polymers: Long-time memory of defect initial data. Discrete & Continuous Dynamical Systems - B, 2011, 15 (2) : 457-473. doi: 10.3934/dcdsb.2011.15.457
[2]

Pavel Krejčí, Jürgen Sprekels. Long time behaviour of a singular phase transition model. Discrete & Continuous Dynamical Systems - A, 2006, 15 (4) : 1119-1135. doi: 10.3934/dcds.2006.15.1119
[3]

Francesca Marcellini. Existence of solutions to a boundary value problem for a phase transition traffic model. Networks & Heterogeneous Media, 2017, 12 (2) : 259-275. doi: 10.3934/nhm.2017011
[4]

Mauro Garavello. Boundary value problem for a phase transition model. Networks & Heterogeneous Media, 2016, 11 (1) : 89-105. doi: 10.3934/nhm.2016.11.89
[5]

Gilles Carbou, Bernard Hanouzet. Relaxation approximation of the Kerr model for the impedance initial-boundary value problem. Conference Publications, 2007, 2007 (Special) : 212-220. doi: 10.3934/proc.2007.2007.212
[6]

Jan Prüss, Vicente Vergara, Rico Zacher. Well-posedness and long-time behaviour for the non-isothermal Cahn-Hilliard equation with memory. Discrete & Continuous Dynamical Systems - A, 2010, 26 (2) : 625-647. doi: 10.3934/dcds.2010.26.625
[7]

Eduard Feireisl, Françoise Issard-Roch, Hana Petzeltová. Long-time behaviour and convergence towards equilibria for a conserved phase field model. Discrete & Continuous Dynamical Systems - A, 2004, 10 (1&2) : 239-252. doi: 10.3934/dcds.2004.10.239
[8]

Yi Zhou, Jianli Liu. The initial-boundary value problem on a strip for the equation of time-like extremal surfaces. Discrete & Continuous Dynamical Systems - A, 2009, 23 (1&2) : 381-397. doi: 10.3934/dcds.2009.23.381
[9]

Xiaoyun Cai, Liangwen Liao, Yongzhong Sun. Global strong solution to the initial-boundary value problem of a 2-D Kazhikhov-Smagulov type model. Discrete & Continuous Dynamical Systems - S, 2014, 7 (5) : 917-923. doi: 10.3934/dcdss.2014.7.917
[10]

Peng Jiang. Unique global solution of an initial-boundary value problem to a diffusion approximation model in radiation hydrodynamics. Discrete & Continuous Dynamical Systems - A, 2015, 35 (7) : 3015-3037. doi: 10.3934/dcds.2015.35.3015
[11]

Haifeng Hu, Kaijun Zhang. Analysis on the initial-boundary value problem of a full bipolar hydrodynamic model for semiconductors. Discrete & Continuous Dynamical Systems - B, 2014, 19 (6) : 1601-1626. doi: 10.3934/dcdsb.2014.19.1601
[12]

Tatsien Li, Libin Wang. Global classical solutions to a kind of mixed initial-boundary value problem for quasilinear hyperbolic systems. Discrete & Continuous Dynamical Systems - A, 2005, 12 (1) : 59-78. doi: 10.3934/dcds.2005.12.59
[13]

Xianpeng Hu, Dehua Wang. The initial-boundary value problem for the compressible viscoelastic flows. Discrete & Continuous Dynamical Systems - A, 2015, 35 (3) : 917-934. doi: 10.3934/dcds.2015.35.917
[14]

Yuguo Lin, Daqing Jiang. Long-time behaviour of a perturbed SIR model by white noise. Discrete & Continuous Dynamical Systems - B, 2013, 18 (7) : 1873-1887. doi: 10.3934/dcdsb.2013.18.1873
[15]

Lingbing He, Claude Le Bris, Tony Lelièvre. Periodic long-time behaviour for an approximate model of nematic polymers. Kinetic & Related Models, 2012, 5 (2) : 357-382. doi: 10.3934/krm.2012.5.357
[16]

Elena Bonetti, Giovanna Bonfanti, Riccarda Rossi. Long-time behaviour of a thermomechanical model for adhesive contact. Discrete & Continuous Dynamical Systems - S, 2011, 4 (2) : 273-309. doi: 10.3934/dcdss.2011.4.273
[17]

Tong Li, Kun Zhao. Global existence and long-time behavior of entropy weak solutions to a quasilinear hyperbolic blood flow model. Networks & Heterogeneous Media, 2011, 6 (4) : 625-646. doi: 10.3934/nhm.2011.6.625
[18]

Irena Lasiecka, To Fu Ma, Rodrigo Nunes Monteiro. Long-time dynamics of vectorial von Karman system with nonlinear thermal effects and free boundary conditions. Discrete & Continuous Dynamical Systems - B, 2018, 23 (3) : 1037-1072. doi: 10.3934/dcdsb.2018141
[19]

Elena Bonetti, Elisabetta Rocca. Global existence and long-time behaviour for a singular integro-differential phase-field system. Communications on Pure & Applied Analysis, 2007, 6 (2) : 367-387. doi: 10.3934/cpaa.2007.6.367
[20]

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 - A, 1999, 5 (2) : 375-390. doi: 10.3934/dcds.1999.5.375

2018 Impact Factor: 1.008

Tools

Metrics

  • PDF downloads (13)
  • HTML views (0)
  • Cited by (11)

Other articles
by authors

[Back to Top]

Copyright © 2019 American Institute of Mathematical Sciences