Decay property of regularity-loss type and nonlinear effects for dissipative timoshenko system

Kentaro Ide, Shuichi Kawashima

Research output: Contribution to journalArticle

58 Citations (Scopus)

Abstract

We consider the initial value problem for a nonlinear version of the dissipative Timoshenko system. This syetem verifies the decay property of regularity-loss type. To overcome this difficulty caused by the regularity-loss property, we employ the time weighed L2 energy method which is combined with the optimal L2 decay estimates for lower order derivatives of solutions. Then we show the global existence and asymptotic decay of solutions under smallness and enough regularity conditions on the initial data. Moreover, we show that the solution approaches the linear diffusion wave expressed in terms of the superposition of the heat kernels as time tends to infinity.

Original languageEnglish
Pages (from-to)1001-1025
Number of pages25
JournalMathematical Models and Methods in Applied Sciences
Volume18
Issue number7
DOIs
Publication statusPublished - 2008 Jul 1
Externally publishedYes

Keywords

  • Asymptotic behavior
  • Decay property of regularity-loss type
  • Dissipative Timoshenko system
  • Time weighted energy method

ASJC Scopus subject areas

  • Modelling and Simulation
  • Applied Mathematics

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