Decay For Solutions To Generalized Semilinear Plate Type Equations With Memory Dissipation

In this paper we discuss the initial value problem of an inertial model for a generalized semi-linear plate type equation with memory in R"(n ? 1).Under suitable assumptions,combining with the result of the corresponding linear problems and using the time-weighted energy method and the contraction mapping theorem,we obtain the global existence and the optimal decay estimates of solutions to the semi-linear problem.In some elementary estimates,we used some of the basic tools from functional analysis and harmonic analysis.Compared with the related results of the literatures,we extend the conclusion of the semi-linear perturbation problem of the plate equation from the integer order derivative estimates to the fractional derivative estimates,and optimize some related estimates.