Existence and uniqueness of solutions for a three-dimensional thermoelastic system
Volume 406 / 2002
Dissertationes Mathematicae 406 (2002), 1-46
MSC: 35Q72, 35K50, 35K60, 74B20.
DOI: 10.4064/dm406-0-1
Abstract
A thermodynamically consistent model of shape memory alloys in three dimensions is studied. The thermoelastic system, based on the strain tensor, its gradient and the absolute temperature, is a generalization of the well-known one-dimensional Falk model. The key assumptions concerning the form of constitutive relations are discussed. The detailed and selfcontained proof of the global-in-time existence and uniqueness of solutions is presented.
