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

Kentaro Ide, Shuichi Kawashima

Research output: Contribution to journalArticle

54 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 - Jul 1 2008

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Nonlinear Effects
Regularity
Decay
Linear Diffusion
Decay of Solutions
Decay Estimates
Initial value problems
Energy Method
Heat Kernel
Regularity Conditions
Global Existence
Superposition
Initial Value Problem
Infinity
Tend
Verify
Derivatives
Derivative
Hot Temperature

All Science Journal Classification (ASJC) codes

  • Modelling and Simulation
  • Applied Mathematics

Cite this

Decay property of regularity-loss type and nonlinear effects for dissipative timoshenko system. / Ide, Kentaro; Kawashima, Shuichi.

In: Mathematical Models and Methods in Applied Sciences, Vol. 18, No. 7, 01.07.2008, p. 1001-1025.

Research output: Contribution to journalArticle

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