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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 and Applied Analysis, 2009, 8 (3) : 1093-1115. doi: 10.3934/cpaa.2009.8.1093
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