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

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.