Global existence and asymptotic decay of solutions to the nonlinear Timoshenko system with memory

Yongqin Liu; Shuichi Kawashima

doi:10.1016/j.na.2013.02.005

Global existence and asymptotic decay of solutions to the nonlinear Timoshenko system with memory

Yongqin Liu, Shuichi Kawashima

Research output: Contribution to journal › Article › peer-review

10 Citations (Scopus)

Abstract

In this paper we consider the initial-value problem for the nonlinear Timoshenko system with a memory term. Due to the regularity-loss property and weak dissipation, we have to assume stronger nonlinearity than usual. By virtue of the semi-group arguments, we obtain the global existence and optimal decay of solutions to the nonlinear problem under smallness and enough regularity assumptions on the initial data, where we employ a time-weighted ^L2 energy method combined with the optimal ^L2 decay of lower-order derivatives of solutions.

Original language	English
Pages (from-to)	1-17
Number of pages	17
Journal	Nonlinear Analysis, Theory, Methods and Applications
Volume	84
DOIs	https://doi.org/10.1016/j.na.2013.02.005
Publication status	Published - 2013 Mar 12
Externally published	Yes

Keywords

Existence and decay
Initial-value problem
Nonlinear Timoshenko system with memory
Regularity-loss type

ASJC Scopus subject areas

Analysis
Applied Mathematics

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abstract = "In this paper we consider the initial-value problem for the nonlinear Timoshenko system with a memory term. Due to the regularity-loss property and weak dissipation, we have to assume stronger nonlinearity than usual. By virtue of the semi-group arguments, we obtain the global existence and optimal decay of solutions to the nonlinear problem under smallness and enough regularity assumptions on the initial data, where we employ a time-weighted L2 energy method combined with the optimal L2 decay of lower-order derivatives of solutions.",

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AU - Liu, Yongqin

AU - Kawashima, Shuichi

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N2 - In this paper we consider the initial-value problem for the nonlinear Timoshenko system with a memory term. Due to the regularity-loss property and weak dissipation, we have to assume stronger nonlinearity than usual. By virtue of the semi-group arguments, we obtain the global existence and optimal decay of solutions to the nonlinear problem under smallness and enough regularity assumptions on the initial data, where we employ a time-weighted L2 energy method combined with the optimal L2 decay of lower-order derivatives of solutions.

AB - In this paper we consider the initial-value problem for the nonlinear Timoshenko system with a memory term. Due to the regularity-loss property and weak dissipation, we have to assume stronger nonlinearity than usual. By virtue of the semi-group arguments, we obtain the global existence and optimal decay of solutions to the nonlinear problem under smallness and enough regularity assumptions on the initial data, where we employ a time-weighted L2 energy method combined with the optimal L2 decay of lower-order derivatives of solutions.

KW - Existence and decay

KW - Initial-value problem

KW - Nonlinear Timoshenko system with memory

KW - Regularity-loss type

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