Global existence and optimal decay rates for the Timoshenko system: The case of equal wave speeds

Naofumi Mori, Jiang Xu, Shuichi Kawashima

Research output: Contribution to journalArticle

13 Citations (Scopus)

Abstract

We first show the global existence and optimal decay rates of solutions to the classical Timoshenko system in the framework of Besov spaces. Due to the non-symmetric dissipation, the general theory for dissipative hyperbolic systems (see [31]) cannot be applied to the Timoshenko system directly. In the case of equal wave speeds, we construct global solutions to the Cauchy problem pertaining to data in the spatially Besov spaces. Furthermore, the dissipative structure enables us to give a new decay framework which pays less attention on the traditional spectral analysis. Consequently, the optimal decay estimates of solution and its derivatives of fractional order are shown by time-weighted energy approaches in terms of low-frequency and high-frequency decompositions. As a by-product, the usual decay estimate of L1(R)-L2(R) type is also shown.

Original languageEnglish
Pages (from-to)1494-1518
Number of pages25
JournalJournal of Differential Equations
Volume258
Issue number5
DOIs
Publication statusPublished - 2015 Jan 1
Externally publishedYes

Fingerprint

Decay Estimates
Wave Speed
Besov Spaces
Decay Rate
Spectrum analysis
Global Existence
Byproducts
Dissipative Structure
Derivatives
Decomposition
Dissipative Systems
Hyperbolic Systems
Fractional Order
Spectral Analysis
Global Solution
Low Frequency
Dissipation
Cauchy Problem
Decay
Decompose

Keywords

  • Critical Besov spaces
  • Global existence
  • Optimal decay estimates
  • Timoshenko system

ASJC Scopus subject areas

  • Analysis

Cite this

Global existence and optimal decay rates for the Timoshenko system : The case of equal wave speeds. / Mori, Naofumi; Xu, Jiang; Kawashima, Shuichi.

In: Journal of Differential Equations, Vol. 258, No. 5, 01.01.2015, p. 1494-1518.

Research output: Contribution to journalArticle

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