留言板

尊敬的读者、作者、审稿人, 关于本刊的投稿、审稿、编辑和出版的任何问题, 您可以本页添加留言。我们将尽快给您答复。谢谢您的支持!

姓名
邮箱
手机号码
标题
留言内容
验证码

一类热弹性板的空间衰减估计

石金诚

石金诚. 一类热弹性板的空间衰减估计 [J]. 应用数学和力学,2022,43(1):115-122 doi: 10.21656/1000-0887.420005
引用本文: 石金诚. 一类热弹性板的空间衰减估计 [J]. 应用数学和力学,2022,43(1):115-122 doi: 10.21656/1000-0887.420005
SHI Jincheng. Spatial Decay Estimates for a Class of Thermoelastic Plates[J]. Applied Mathematics and Mechanics, 2022, 43(1): 115-122. doi: 10.21656/1000-0887.420005
Citation: SHI Jincheng. Spatial Decay Estimates for a Class of Thermoelastic Plates[J]. Applied Mathematics and Mechanics, 2022, 43(1): 115-122. doi: 10.21656/1000-0887.420005

一类热弹性板的空间衰减估计

doi: 10.21656/1000-0887.420005
基金项目: 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)
详细信息
    作者简介:

    石金诚(1983—),男,讲师,硕士(E-mail: hning0818@163.com

  • 中图分类号: O175.29

Spatial Decay Estimates for a Class of Thermoelastic Plates

  • 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。

  • [1] BOLEY B A. The determination of temperature, stresses, and deflections in two-dimensional thermoelastic problems[J]. Journal of the Aeronautical Sciences, 1956, 23(1): 67-75. doi: 10.2514/8.3503
    [2] HORGAN C O. Recent developments concerning Saint-Venant’s principle: an update[J]. Applied Mechanics Reviews, 1989, 42(11): 295-302. doi: 10.1115/1.3152414
    [3] KNOWLES J K. An energy estimate for the biharmonic equation and its application to Saint-Venant’s principle in plane elastostatics[J]. Indian Journal of Pure and Applied Mathematics, 1983, 14(7): 791-805.
    [4] PAYNE L E, SCHAEFER P W. Some Phragmén-Lindelöf type results for the biharmonic equation[J]. Zeitschrift für Angewandte Mathematik und Physik, 1994, 45(3): 414-432. doi: 10.1007/BF00945929
    [5] LIN C H. Spatial decay estimates and energy bounds for the Stokes flow equation[J]. Stability and Applied Analysis of Continuous Media, 1992, 2: 249-264.
    [6] FLAVIN J N. On Knowles’ version of Saint-Venant’s principle in two-dimensional elastostatics[J]. Archive for Rational Mechanics and Analysis, 1973, 53: 366-375.
    [7] HORGAN C O. Decay estimates for the biharmonic equation with applications to Saint-Venant’s principles in plane elasticity and Stokes flows[J]. Quarterly of Applied Mathematics, 1989, 47(1): 147-157. doi: 10.1090/qam/987903
    [8] LIU Y, LIN C H. Phragmén-Lindelöf type alternative results for the Stokes flow equation[J]. Mathematical Inequalities & Applications, 2006, 9(4): 671-694.
    [9] LI Y F, LIN C H. Spatial decay for solutions to 2-D Boussinesq system with variable thermal diffusivity[J]. Acta Applicandae Mathematica, 2018, 154: 111-130. doi: 10.1007/s10440-017-0136-z
    [10] 李远飞, 石金诚, 曾鹏. 三维柱体上调和方程的二则一结果[J]. 海南大学学报自然科学版, 2020, 38(1): 6-12. (LI Yuanfei, SHI Jincheng, ZENG Peng. Phragmén-Lindelöf alternative type results for harmonic equation in a 3D cylinder[J]. Natural Science Journal of Hainan University, 2020, 38(1): 6-12.(in Chinese)
    [11] 李远飞. 在一个半无穷柱体上的非标准Stokes流体方程的二择一问题[J]. 应用数学和力学, 2020, 41(4): 406-419. (LI Yuanfei. Phragmén-Lindelöf type results for non-standard Stokes flow equations around semi-infinite cylinder[J]. Applied Mathematics and Mechanics, 2020, 41(4): 406-419.(in Chinese)
    [12] 李远飞, 曾鹏. 具有非线性边界条件的调和方程在无界区域上的Phragmén-Lindelöf二择性结果[J]. 河南大学学报(自然科学版), 2020, 50(3): 365-372. (LI Yuanfei, ZENG Peng. Phragmén-Lindelöf alternative type results for the harmonic equation with nonlinear boundary conditions in an unbounded region[J]. Journal of Henan University (Natural Science), 2020, 50(3): 365-372.(in Chinese)
    [13] 李远飞, 张旖. 一些热传导理论中的伪抛物方程的Phragmén-Lindelöf二择性结果[J]. 数学的实践与认识, 2020, 50(12): 220-232. (LI Yuanfei, ZHANG Yi. Phragmén-Lindelöf alternative type results for the pseudo-parabolic equation in some theories of heat conduction[J]. Mathematics in Practice and Theory, 2020, 50(12): 220-232.(in Chinese)
    [14] 李远飞, 肖胜中, 郭连红, 等. 一类二阶拟线性瞬态方程组的Phragmén-Lindelöf型二择性结果[J]. 吉林大学学报(理学版), 2020, 58(5): 1047-1054. (LI Yuanfei, XIAO Shengzhong, GUO Lianhong, et al. Phragmén-Lindelöf type alternative results for a class of second order quasilinear transient equations[J]. Journal of Jilin University(Science Edition), 2020, 58(5): 1047-1054.(in Chinese)
    [15] 李远飞, 李志青. 具有非线性边界条件的瞬态热传导方程的二择一结果[J]. 数学物理学报, 2020, 40A(5): 1248-1258. (LI Yuanfei, LI Ziqing. Phragmén-Lindelöf type results for transient heat conduction equation with nonlinear boundary conditions[J]. Acta Mathematica Scientia, 2020, 40A(5): 1248-1258.(in Chinese) doi: 10.3969/j.issn.1003-3998.2020.05.012
    [16] LIU Y, CHEN W H. Asymptotic profiles of solutions for regularity-loss-type generalized thermoelastic plate equations and their applications[J]. Zeitschrift für Angewandte Mathematik und Physik, 2020, 71(3): 15-55.
  • 加载中
计量
  • 文章访问数:  376
  • HTML全文浏览量:  157
  • PDF下载量:  27
  • 被引次数: 0
出版历程
  • 收稿日期:  2021-01-07
  • 修回日期:  2021-03-03
  • 网络出版日期:  2021-11-15
  • 刊出日期:  2022-01-01

目录

    /

    返回文章
    返回