Stability of abstract thermoelastic systems with inertial terms

Hugo D. Fernández Sare, Zhuangyi Liu, Reinhard Racke

Research output: Contribution to journalArticlepeer-review

Abstract

We investigate coupled systems of thermoelastic type in a general abstract form both modeling Fourier and Cattaneo type heat conduction. In particular we take into account a possible inertial term. A complete picture of the regions of exponential stability resp. non-exponential stability for the arising parameters (two from the type of thermoelastic system, one from the inertial term) is given. The regions of loss of exponential stability, while moving from the Fourier to the Cattaneo law, are thus clearly recognized and interestingly large. The polynomial stability in regions of non-exponential stability is also characterized.

Original languageEnglish (US)
Pages (from-to)7085-7134
Number of pages50
JournalJournal of Differential Equations
Volume267
Issue number12
DOIs
StatePublished - Dec 5 2019

Keywords

  • Cattaneo law of heat conduction
  • Exponential stability
  • Fourier law of heat conduction
  • General parameter system
  • Inertial term
  • Polynomial stability

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