Premium
Global existence to a three‐dimensional non‐linear thermoelasticity system arising in shape memory materials
Author(s) -
Pawłow Irena,
Zaja̧czkowski Wojciech M.
Publication year - 2005
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.574
Subject(s) - mathematics , regular polygon , dissipation , viscoelasticity , elastic energy , mathematical analysis , thermal conduction , energy (signal processing) , shape memory alloy , fixed point theorem , point (geometry) , linear system , geometry , physics , computer science , thermodynamics , statistics , artificial intelligence
Abstract This paper is concerned with the unique global solvability of a three‐dimensional (3‐D) non‐linear thermoelasticity system arising from the study of shape memory materials. The system consists of the coupled evolutionary problems of viscoelasticity with non‐convex elastic energy and non‐linear heat conduction with mechanical dissipation. The present paper extends the previous 2‐D existence result of the authors Reference [1] to 3‐D case. This goal is achieved by means of the Leray–Schauder fixed point theorem using technique based on energy arguments and DeGiorgi method. Copyright © 2004 John Wiley & Sons, Ltd.