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
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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 -