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本文主要研究一类带旋转惯性项及时间延迟性耗散结构的板方程的解的衰减及正则性损失问题。由于方程中的记忆项含有$u_t$,传统的方法不能直接应用。为了克服这个困难,作者将问题转化为一类具有特殊形式的非齐次方程。针对非齐次项进行估计,得到了方程解的衰减及
毛仕宽*，
程琼
（ 华北电力大学数理学院,北京 102206； ）
摘要： 本文主要研究一类带旋转惯性项及时间延迟性耗散结构的板方程的解的衰减及正则性损失问题。由于方程中的记忆项含有$u_t$,传统的方法不能直接应用。为了克服这个困难,作者将问题转化为一类具有特殊形式的非齐次方程。针对非齐次项进行估计,得到了方程解的衰减及正则性损失的相关估计。本文的另一个新颖之处：与相关传统文献的结果相比较,本文所研究的方程的解的衰减和正则性损失都由高频部分决定。因此,不需要对初值作$L^1(mathbb{R}^n)$假设,就可以得到类似的结论。
关键词： 偏微分方程,板方程,记忆项,衰减,正则性损失,频率空间中的逐点估计
MAO Shi-Kuan*， CHENG Qiong
（ School of Mathemaics and Physics, North China Electric Power University, Beijing 102206； ）
Abstract： 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.
Keywords： partial differential equation, plate equation, memory, decay, regularity-loss property, pointwise estimates in frequency space.
作者简介： MAO Shikuan, male, associate professor, major research direction: Partial Differential Equations.
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