Unique solvability of a nonlinear thermoviscoelasticity system in Sobolev space with a mixed norm

Irena Pawłow; Wojciech M. Zajączkowski

doi:10.3934/dcdss.2011.4.441

Article Contents

2011, Volume 4, Issue 2: 441-466. Doi: 10.3934/dcdss.2011.4.441

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Unique solvability of a nonlinear thermoviscoelasticity system in Sobolev space with a mixed norm

Irena Pawłow¹ and
Wojciech M. Zajączkowski²

1.
System Research Institute, Polish Academy of Sciences, Newelska 6, 01-447 Warsaw
2.
Institute of Mathematics, Polish Academy of Sciences, Śniadeckich 8, 00-656 Warsaw

Received: February 2009

Published: April 2011

Abstract / Introduction Related Papers Cited by

Abstract

In this paper we study a nonlinear thermoviscoelasticity system within the framework of parabolic theory in anisotropic Sobolev spaces with a mixed norm. The application of such a framework allows to generalize the previous results by admitting stronger thermomechanical nonlinearity and a broader class of solution spaces.

Keywords:

Nonlinear thermoviscoelasticity,
shape memory,
parabolic theory,
anisotropic Sobolev spaces with a mixed norm.

Mathematics Subject Classification: Primary 74B20, 35K50; Secondary 35Q72, 74F05.

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