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

Yongqin Liu, Shuichi Kawashima

Research output: Contribution to journalArticle

7 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 languageEnglish
Pages (from-to)1-17
Number of pages17
JournalNonlinear Analysis, Theory, Methods and Applications
Volume84
DOIs
Publication statusPublished - 2013 Mar 12
Externally publishedYes

Fingerprint

Decay of Solutions
Initial value problems
Global Existence
Nonlinear systems
Regularity
Derivatives
Data storage equipment
Memory Term
Energy Method
Initial Value Problem
Nonlinear Problem
Dissipation
Semigroup
Nonlinearity
Decay
Derivative

Keywords

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

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

Cite this

@article{b745d7f4d59c49dcb1fe0e3122423a45,
title = "Global existence and asymptotic decay of solutions to the nonlinear Timoshenko system with memory",
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.",
keywords = "Existence and decay, Initial-value problem, Nonlinear Timoshenko system with memory, Regularity-loss type",
author = "Yongqin Liu and Shuichi Kawashima",
year = "2013",
month = "3",
day = "12",
doi = "10.1016/j.na.2013.02.005",
language = "English",
volume = "84",
pages = "1--17",
journal = "Nonlinear Analysis, Theory, Methods and Applications",
issn = "0362-546X",
publisher = "Elsevier Limited",

}

TY - JOUR

T1 - Global existence and asymptotic decay of solutions to the nonlinear Timoshenko system with memory

AU - Liu, Yongqin

AU - Kawashima, Shuichi

PY - 2013/3/12

Y1 - 2013/3/12

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

UR - http://www.scopus.com/inward/record.url?scp=84874710215&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84874710215&partnerID=8YFLogxK

U2 - 10.1016/j.na.2013.02.005

DO - 10.1016/j.na.2013.02.005

M3 - Article

AN - SCOPUS:84874710215

VL - 84

SP - 1

EP - 17

JO - Nonlinear Analysis, Theory, Methods and Applications

JF - Nonlinear Analysis, Theory, Methods and Applications

SN - 0362-546X

ER -