Decay estimate and global existence of a semilinear Mindlin-Timoshenko plate system with full frictional damping in the whole space

Abstract

In this paper, we are interested in a semilinear Mindlin-Timoshenko system with an irrotationality condition for the angle variables. Under the smallness assumption on the initial data, the decay rate of solutions is obtained by using both the multiplier method in the Fourier space and the fundamental solution method. Moreover, we also prove the global existence of solutions by the standard method.