American Institute of Mathematical Sciences

Advanced
  • Previous Article
    $L^2$-concentration phenomenon for Zakharov system below energy norm II
  • CPAA Home
  • This Issue
  • Next Article
    Well-posedness and stability of classical solutions to the multidimensional full hydrodynamic model for semiconductors
May  2009, 8(3): 1093-1115. doi: 10.3934/cpaa.2009.8.1093

A quasilinear thermoviscoelastic system for shape memory alloys with temperature dependent specific heat

Shuji Yoshikawa 1, , Irena Pawłow 2, and  Wojciech M. Zajączkowski 3,

1. 

Department of Business Administration, Ube National College of Technology, 2-14-1 Tokiwadai Ube, Yamaguchi, 755-8555, Japan
2. 

System Research Institute, Polish Academy of Sciences, Newelska 6, 01-447 Warsaw
3. 

Institute of Mathematics, Polish Academy of Sciences, Śniadeckich 8, 00-656 Warsaw

Received  May 2008 Revised  November 2008 Published  February 2009

This article extends the previous author's paper [28] on the existence of solutions to a quasilinear thermoviscoelasticity system arising in shape memory alloys. In the present setup we admit a modified energy equation with temperature growing specific heat. Due to such a modification we can solve the problem with stronger thermomechanical nonlinearity which was left open in [28].
Keywords: parabolic system, Shape memory, phase transition., thermoviscoelastic.
Mathematics Subject Classification: Primary: 74B20, 35K50; Secondary: 35Q72, 74F0.
Citation: Shuji Yoshikawa, Irena Pawłow, Wojciech M. Zajączkowski. A quasilinear thermoviscoelastic system for shape memory alloys with temperature dependent specific heat. Communications on Pure & Applied Analysis, 2009, 8 (3) : 1093-1115. doi: 10.3934/cpaa.2009.8.1093
[1]

Federico Mario Vegni. Dissipativity of a conserved phase-field system with memory. Discrete & Continuous Dynamical Systems - A, 2003, 9 (4) : 949-968. doi: 10.3934/dcds.2003.9.949
[2]

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
[3]

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
[4]

Matteo Novaga, Enrico Valdinoci. The geometry of mesoscopic phase transition interfaces. Discrete & Continuous Dynamical Systems - A, 2007, 19 (4) : 777-798. doi: 10.3934/dcds.2007.19.777
[5]

Alain Miranville. Some mathematical models in phase transition. Discrete & Continuous Dynamical Systems - S, 2014, 7 (2) : 271-306. doi: 10.3934/dcdss.2014.7.271
[6]

Michel Frémond, Elisabetta Rocca. A model for shape memory alloys with the possibility of voids. Discrete & Continuous Dynamical Systems - A, 2010, 27 (4) : 1633-1659. doi: 10.3934/dcds.2010.27.1633
[7]

Toyohiko Aiki. The position of the joint of shape memory alloy and bias springs. Discrete & Continuous Dynamical Systems - S, 2011, 4 (2) : 239-246. doi: 10.3934/dcdss.2011.4.239
[8]

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
[9]

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
[10]

Monica Conti, Stefania Gatti, Alain Miranville. A singular cahn-hilliard-oono phase-field system with hereditary memory. Discrete & Continuous Dynamical Systems - A, 2018, 38 (6) : 3033-3054. doi: 10.3934/dcds.2018132
[11]

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
[12]

Jun Yang. Coexistence phenomenon of concentration and transition of an inhomogeneous phase transition model on surfaces. Discrete & Continuous Dynamical Systems - A, 2011, 30 (3) : 965-994. doi: 10.3934/dcds.2011.30.965
[13]

Mauro Garavello, Benedetto Piccoli. Coupling of microscopic and phase transition models at boundary. Networks & Heterogeneous Media, 2013, 8 (3) : 649-661. doi: 10.3934/nhm.2013.8.649
[14]

Emanuela Caliceti, Sandro Graffi. An existence criterion for the $\mathcal{PT}$-symmetric phase transition. Discrete & Continuous Dynamical Systems - B, 2014, 19 (7) : 1955-1967. doi: 10.3934/dcdsb.2014.19.1955
[15]

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
[16]

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
[17]

I-Liang Chern, Chun-Hsiung Hsia. Dynamic phase transition for binary systems in cylindrical geometry. Discrete & Continuous Dynamical Systems - B, 2011, 16 (1) : 173-188. doi: 10.3934/dcdsb.2011.16.173
[18]

Mauro Garavello, Francesca Marcellini. The Riemann Problem at a Junction for a Phase Transition Traffic Model. Discrete & Continuous Dynamical Systems - A, 2017, 37 (10) : 5191-5209. doi: 10.3934/dcds.2017225
[19]

Maya Briani, Benedetto Piccoli. Fluvial to torrential phase transition in open canals. Networks & Heterogeneous Media, 2018, 13 (4) : 663-690. doi: 10.3934/nhm.2018030
[20]

Pierluigi Colli, Antonio Segatti. Uniform attractors for a phase transition model coupling momentum balance and phase dynamics. Discrete & Continuous Dynamical Systems - A, 2008, 22 (4) : 909-932. doi: 10.3934/dcds.2008.22.909

2018 Impact Factor: 0.925

Tools

Metrics

  • PDF downloads (24)
  • HTML views (0)
  • Cited by (5)

Other articles
by authors

[Back to Top]

Copyright © 2020 American Institute of Mathematical Sciences