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Lp–Lq decay estimates for Cauchy problems of linear thermoelastic systems with second sound in three dimensions

Published online by Cambridge University Press:  12 July 2007

Ya-Guang Wang  and
Lin Yang
Ya-Guang Wang
Affiliation:
Department of Mathematics, Shanghai Jiao Tong University, Shanghai 200240, People's Republic of China
Lin Yang
Affiliation:
College of mathematics, Hunan University, Changsha 410082, People's Republic of China ([email protected])
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Abstract

Lp–Lq decay estimates of solutions to Cauchy problems of linear thermoelastic systems with second sound in three spatial variables are studied. By carefully analysis of the different effects of higher, middle and lower frequencies in phase space, the asymptotic behaviour of characteristic roots of coefficient matrices is obtained. Then, with the help of the information on characteristic roots and the interpolation theorem, a decay estimate of parabolic type for the coupled system of the potential part of displacement, temperature and heat flux is obtained. Finally, Lp–Lq decay estimates of hyperbolic type for the original thermoelastic systems with second sound are obtained.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 136 , Issue 1 , February 2006 , pp. 189 - 207
Copyright
Copyright © Royal Society of Edinburgh 2006

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