Decay property of the Timoshenko-Cattaneo system

Naofumi Mori, Shuichi Kawashima

Research output: Contribution to journalArticle

7 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 - May 1 2016

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Decay
Heat conduction
Thermal effects
Differential equations
Data storage equipment
Decay Estimates
Regularity
Heat Conduction
Dissipative Structure
Stability number
Pointwise Estimates
Thermal Effects
Hyperbolic Equations
Low Frequency
Differential equation
Model

All Science Journal Classification (ASJC) codes

  • Analysis
  • Applied Mathematics

Cite this

Decay property of the Timoshenko-Cattaneo system. / Mori, Naofumi; Kawashima, Shuichi.

In: Analysis and Applications, Vol. 14, No. 3, 01.05.2016, p. 393-413.

Research output: Contribution to journalArticle

Mori, Naofumi ; Kawashima, Shuichi. / Decay property of the Timoshenko-Cattaneo system. In: Analysis and Applications. 2016 ; Vol. 14, No. 3. pp. 393-413.
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