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非Fourier温度场分布的奇摄动解

包立平 李文彦 吴立群

包立平, 李文彦, 吴立群. 非Fourier温度场分布的奇摄动解[J]. 应用数学和力学, 2019, 40(5): 536-545. doi: 10.21656/1000-0887.390112
引用本文: 包立平, 李文彦, 吴立群. 非Fourier温度场分布的奇摄动解[J]. 应用数学和力学, 2019, 40(5): 536-545. doi: 10.21656/1000-0887.390112
BAO Liping, LI Wenyan, WU Liqun. Singularly Perturbed Solutions of NonFourier Temperature Field Distribution in Single-Layer Materials[J]. Applied Mathematics and Mechanics, 2019, 40(5): 536-545. doi: 10.21656/1000-0887.390112
Citation: BAO Liping, LI Wenyan, WU Liqun. Singularly Perturbed Solutions of NonFourier Temperature Field Distribution in Single-Layer Materials[J]. Applied Mathematics and Mechanics, 2019, 40(5): 536-545. doi: 10.21656/1000-0887.390112

非Fourier温度场分布的奇摄动解

doi: 10.21656/1000-0887.390112
基金项目: 国家自然科学基金(51175134);浙江省重点自然科学基金(LZ15E050004)
详细信息
    作者简介:

    包立平(1962—),男,副教授,博士(通讯作者. E-mail: baolp@hdu.edu.cn);李文彦(1993—),女,硕士生.

  • 中图分类号: TK12

Singularly Perturbed Solutions of NonFourier Temperature Field Distribution in Single-Layer Materials

Funds: The National Natural Science Foundation of China(51175134)
  • 摘要: 应用非Fourier热传导定律构建了单层材料中温度场模型,即一类在无界域上带小参数的奇摄动双曲方程,通过奇摄动展开方法,得到了该问题的渐近解.首先应用奇摄动方法得到了该问题的外解和边界层矫正项,通过对内解和外解的最大模估计和关于时间导数的最大模估计以及线性抛物方程理论,得到了内外解的存在唯一性,从而得到了解的形式渐近展开式.通过余项估计,给出了渐近解的L2估计,得到了渐近解的一致有效性,从而得到了无界域上温度场的分布.通过奇摄动分析,给出了非Fourier 温度场与Fourier 温度场的关系,描述了非Fourier温度场的具体形态.
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出版历程
  • 收稿日期:  2018-04-11
  • 修回日期:  2018-11-12
  • 刊出日期:  2019-05-01

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