On the plate equation with nonstationary stochastic process coefficients
On the plate equation with nonstationary stochastic process coefficients
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DOI：
10.1002/zamm.202000205
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发表时间：
2021-12
期刊：
影响因子：
--
通讯作者：
Xiaojun Lu
中科院分区：
文献类型：
--
作者：
Xiaojun Lu
在力学中，在研究板的振动时，我们经常遇到来自内外环境的随机扰动，如材料的不均匀性、温度的不稳定波动等。在这方面，用带随机系数的板方程来模拟各种扰动的随机性。本文主要研究随机板方程解的正则性，特别是退化系数和振荡系数对主算子的联合影响。我们应用了微局部分析和随机分析的尖端技术来探索正则性损失的上界。此外，为了证明估计的最优性，构造了适当的周期系数反例，通过谐波分析和不稳定性参数来显示正则性损失的下界。
In mechanics, while investigating the vibration of plates, we are frequently confronted with random perturbations from both internal and external environments, such as inhomogeneous materials, unstable temperature fluctuation, etc. In this respect, the plate equation with stochastic coefficients is used for modeling the randomness from various perturbations. Current paper is concerned with the regularity behavior of the solution of the stochastic plate equation, in particular, the joint influence from the degenerating and oscillating coefficients on the principal operator is of prime consideration. We apply the sophisticated techniques from microlocal analysis and stochastic analysis to explore the upper bound of loss of regularity. Furthermore, in order to demonstrate the optimality of the estimates, appropriate counter‐examples with periodic coefficients are constructed to show the lower bound of loss of regularity by the application of harmonic analysis and instability arguments.