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 | |
| Publication status | Published - 2013 Mar 12 |
| Externally published | Yes |
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Keywords
- Existence and decay
- Initial-value problem
- Nonlinear Timoshenko system with memory
- Regularity-loss type
ASJC Scopus subject areas
- Analysis
- Applied Mathematics
Cite this
Global existence and asymptotic decay of solutions to the nonlinear Timoshenko system with memory. / Liu, Yongqin; Kawashima, Shuichi.
In: Nonlinear Analysis, Theory, Methods and Applications, Vol. 84, 12.03.2013, p. 1-17.Research output: Contribution to journal › Article
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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 -