关键词： 板方程, 记忆, 衰变估计, 正则性损耗项

Abstract:

The initial value problem of the semi-linear plate equation with memory in multi-dimension Rⁿ(n≥1) is studied.In the Fourier space,we obtain the decay estimates of solutions to the linear problem.And through introducing a set of time-weighted Sobolev  spaces and applying the contraction mapping theorem,we obtain the global in-time existence and the optimal decay estimates of solutions to the semi-linear problem under smallness assumption on the initial data.

Key words: plate equation, memory, decay estimates, regularity-loss type