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| In this paper an inertial model for a plate equation with time-delay dissipation in $mathbb{R}^n (nge1)$ is considered, and the decay estimate as well as the regularity-loss property for this type of equation are studied. Due to the presence of the $u_t$ in the memory term, the usual method could not be used. By rounding this difficulty, the problem is transfered to a special inhomogeneous problem with the usual type of memory term. Then the result is obtained by a somewhat different argument which is used to deal with the inhomogeneous term. Another novelty of this paper is that both the decay and regularity are controlled by high frequency, compared with the results in the literatures. Thus, a similar result holds without the $L^1(mathbb{R}^n)$ assumption for the initial data. |
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| Keywords:partial differential equation, plate equation, memory, decay, regularity-loss property, pointwise estimates in frequency space. |
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