Decay property of the Timoshenko-Cattaneo system

Naofumi Mori, Shuichi Kawashima

Research output: Contribution to journalArticlepeer-review

8 Citations (Scopus)

Abstract

We study the Timoshenko system with Cattaneo's type heat conduction in the one-dimensional whole space. We investigate the dissipative structure of the system and derive the optimal L2 decay estimate of the solution in a general situation. Our decay estimate is based on the detailed pointwise estimate of the solution in the Fourier space. We observe that the decay property of our Timoshenko-Cattaneo system is of the regularity-loss type. This decay property is a little different from that of the dissipative Timoshenko system (see [K. Ide, K. Haramoto and S. Kawashima, Decay property of regularity-loss type for dissipative Timoshenko system, Math. Models Methods Appl. Sci. 18 (2008) 647-667]) in the low frequency region. However, in the high frequency region, it is just the same as that of the Timoshenko-Fourier system (see [N. Mori and S. Kawashima, Decay property for the Timoshenko system with Fourier's type heat conduction, J. Hyperbolic Differential Equations 11 (2014) 135-157]) or the dissipative Timoshenko system (see [K. Ide, K. Haramoto and S. Kawashima, Decay property of regularity-loss type for dissipative Timoshenko system, Math. Models Methods Appl. Sci. 18 (2008) 647-667]), although the stability number is different. Finally, we study the decay property of the Timoshenko system with the thermal effect of memory-type by reducing it to the Timoshenko-Cattaneo system.

Original languageEnglish
Pages (from-to)393-413
Number of pages21
JournalAnalysis and Applications
Volume14
Issue number3
DOIs
Publication statusPublished - 2016 May 1
Externally publishedYes

Keywords

  • asymptotic behavior
  • decay property
  • pointwise estimate in the Fourier space
  • regularity-loss type
  • Timoshenko system with thermal effects

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

Fingerprint Dive into the research topics of 'Decay property of the Timoshenko-Cattaneo system'. Together they form a unique fingerprint.

Cite this