数学物理学报 ›› 2021, Vol. 41 ›› Issue (4): 1042-1052.

• 论文 • 上一篇    下一篇

热弹性方程的快速增长或衰减估计

李远飞*(),石金诚,朱慧珊,黄诗淇   

  1. 广东财经大学华商学院应用数学系 广州 511300
  • 收稿日期:2020-10-20 出版日期:2021-08-26 发布日期:2021-08-09
  • 通讯作者: 李远飞 E-mail:liqfd@163.com
  • 基金资助:
    广东省普通高校重点项目(自然科学)(2019KZDXM042);广州华商学院科研团队项目(2021HSKT01)

Fast Growth or Decay Estimates of Thermoelastic Equations in an External Domain

Yuanfei Li*(),Jincheng Shi,Huishan Zhu,Shiqi Huang   

  1. Department of Apllied Mathematics, Huashang College Guangdong University of Finance & Economics, Guangzhou 511300
  • Received:2020-10-20 Online:2021-08-26 Published:2021-08-09
  • Contact: Yuanfei Li E-mail:liqfd@163.com
  • Supported by:
    Key Projects of Colleges and Universities in Guangdong Province(Natural Science)(2019KZDXM042);the Science Research Team Project in Guangzhou Huashang College(2021HSKT01)

摘要:

考虑了定义在三维球体外部区域上的Ⅲ型热弹性方程,其中假设方程的解在球体边界上满足一定的边界条件.通过对边界条件做出一定约束之后,在能量表达式中设置一个任意的大于零的参数,利用能量分析法和微分不等式技术,获得了解随距原点的距离的快速增长率或衰减率.在衰减的情况下,证明了解对系数的连续依赖性.

关键词: Ⅲ型热弹性方程, 衰减率, 增长率, 连续依赖性

Abstract:

The Thermoelastic equation of type Ⅲ defined on the outer region of a three-dimensional sphere is considered. It is assumed that the solution of the equation satisfies certain boundary conditions at the boundary of the sphere. By setting an arbitrary parameter greater than zero in the energy expression after making certain constraints on the boundary conditions, the fast growth rate or decay rate of the solution with the distance from the origin is obtained by using energy analysis method and differential inequality technology. In the case of decay, the continuous dependence of solutions on coefficients is proved.

Key words: Type Ⅲ thermoelastic equation, Decay rate, Growth rate, Continuous dependence

中图分类号: 

  • O175.29