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Unique global solvability in two-dimensional non-linear thermoelasticity

✍ Scribed by Irena Pawłow; Wojciech M. Zaja̧czkowski

Publisher
John Wiley and Sons
Year
2005
Tongue
English
Weight
292 KB
Volume
28
Category
Article
ISSN
0170-4214

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✦ Synopsis

Abstract

The paper is concerned with initial‐boundary value problem in two‐dimensional (2‐D) non‐linear thermoelasticity which arises as a mathematical model of shape memory alloys. The problem has the form of viscoelasticity system with fourth order capillarity‐like term coupled with heat conduction equation with mechanical dissipation.

The corresponding elastic energy is a nonconvex multiple‐well function of strain, with the shape changing qualitatively with temperature. Under assumption on the growth of this energy with respect to temperature we prove global in time existence and uniqueness of solutions for large data. The existence proof is based on parabolic decomposition of the elasticity system and application of the Leray–Schauder fixed point theorem. The main part of the proof consists in deriving a priori Hölder estimates by successive improvement of energy estimates. Copyright © 2004 John Wiley & Sons, Ltd.

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