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Continuum Mechanics and Thermodynamics

, Volume 29, Issue 3, pp 731–746 | Cite as

Well-posedness and exponential decay for a porous thermoelastic system with second sound and a time-varying delay term in the internal feedback

  • Wenjun Liu
  • Miaomiao Chen
Original Article

Abstract

In this paper, we study the well-posedness and exponential decay for the porous thermoelastic system with the heat conduction given by Cattaneo’s law and a time-varying delay term, the coefficient of which is not necessarily positive. Using the semigroup arguments and variable norm technique of Kato, we first prove that the system is well-posed under a certain condition on the weight of the delay term, the weight of the elastic damping term and the speed of the delay function. By introducing a suitable energy and an appropriate Lyapunov functional, we then establish an exponential decay rate result.

Keywords

Porous thermoelastic system Elastic damping Time-varying delay Decay 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2017

Authors and Affiliations

  1. 1.College of Mathematics and StatisticsNanjing University of Information Science and TechnologyNanjingChina

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