一类热弹性板的空间衰减估计  

Spatial Decay Estimates for a Class of Thermoelastic Plates

作　　者：石金诚 SHI Jincheng(School of Data Science,Guangzhou Huashang College,Guangzhou 511300,P.R.China)

机构地区：[1]广州华商学院数据科学学院,广州511300

出　　处：《应用数学和力学》2022年第1期115-122,共8页Applied Mathematics and Mechanics

基　　金：国家自然科学基金(11371175);广东普通高校重点科研项目(自然科学)(2019KZDXM042)。

摘　　要：研究了二维空间中半无限带形区域上一类含有双调和算子的热弹性系统板解的空间性质.首先构造一个能量表达式,然后利用微分不等式技术,推导出该能量表达式是可由它本身的一阶导数控制的微分不等式,最后得到解的空间衰减估计.该结果可看成是Saint-Venant原则在双曲抛物耦合双调和方程组上的应用.The spatial properties of solutions for a class of thermoelastic plates with biharmonic operators were studied in a semi-infinite strip in R2. Firstly, an energy expression was constructed. Then, by means of the differential inequality technique, a differential inequality whose energy expression can be controlled with its 1 st derivative was derived. Finally,the spatial decay estimates of the solution were obtained. The result can be regarded as an application of the Saint-Venant principle to hyperbolic parabolic coupled biharmonic equations.

关 键 词：弹性板 空间衰减 Saint-Venant原则 双调和方程 

分 类 号：O175.29[理学—数学]