Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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$ L^{p}-L^{q}$ decay estimates for the Cauchy problem of linear thermoelastic systems with second sound in one space variable

Authors: Lin Yang and Ya-Guang Wang
Journal: Quart. Appl. Math. 64 (2006), 1-15
MSC (2000): Primary 35Q30, 35A21
Published electronically: January 24, 2006
MathSciNet review: 2211374
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Abstract: $ L^p-L^q$ decay estimates of solutions to the Cauchy problem of linear thermoelastic systems with second sound in one space variable will be studied in this paper. First, by dividing the frequency of phase space of the Fourier transformation into different regions, the asymptotic behavior of characteristic roots of the coefficient matrix is obtained by carefully analyzing the effect of the different regions. Second, with the help of the information on the characteristic roots and by using the interpolation theorem, the $ L^{p}-L^{q}$ decay estimate of solutions to the Cauchy problem of the linear thermoelastic system with second sound in one space variable is obtained.

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Additional Information

Lin Yang
Affiliation: College of Mathematics and Economics, Hunan University, Changsha 410082, China
Email: linyang822@yahoo.com.cn

Ya-Guang Wang
Affiliation: Department of Mathematics, Shanghai Jiao Tong University, Shanghai 200240, China

DOI: https://doi.org/10.1090/S0033-569X-06-00989-6
Keywords: $L^{p}-L^{q}$ decay estimates, Cauchy problems, thermoelasticity with second sound
Received by editor(s): January 1, 2004
Published electronically: January 24, 2006
Additional Notes: This work is partially supported by the HNUF, the NSFC, and Shanghai Science and Technology Committee grant 03QMH1407
Article copyright: © Copyright 2006 Brown University

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