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

作者：Liu, Yongqin^*; Kawashima, Shuichi

来源：Nonlinear Analysis-Theory Methods & Applications, 2013, 84: 1-17.

DOI：10.1016/j.na.2013.02.005

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

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 L-2 energy method combined with the optimal L-2 decay of lower-order derivatives of solutions.

• 出版日期2013-6
• 单位华北电力大学（保定）; 华北电力大学