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Spectral analysis and stability of thermoelastic Bresse system with second sound and boundary viscoelastic damping
Author(s) -
Han ZhongJie,
Xu GenQi
Publication year - 2013
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.3052
Subject(s) - thermoelastic damping , viscoelasticity , boundary (topology) , mathematics , mathematical analysis , stability (learning theory) , boundary value problem , exponential stability , spectrum (functional analysis) , energy (signal processing) , fourier transform , physics , classical mechanics , thermal , thermodynamics , quantum mechanics , computer science , statistics , nonlinear system , machine learning
In this paper, we consider the energy decay rate of a thermoelastic Bresse system with variable coefficients. Assume that the thermo‐propagation in the system satisfies the Cattaneo's law, which can eliminate the paradox of infinite speed of thermal propagation in the assumption of the Fourier's law in the classical theory of thermoelasticity. Meanwhile, we also discuss the effect of a boundary viscoelastic damping on the stability of this system. By a detailed spectral analysis, we obtain the expressions of the spectrum and deduce some spectral properties of the system. Then based on the distribution of the spectrum, we prove that the energy of the system with a boundary viscoelastic damping decays exponentially. However, it no longer decays exponentially if there is no boundary damping. Copyright © 2013 John Wiley & Sons, Ltd.