数学物理学报(英文版) ›› 2011, Vol. 31 ›› Issue (4): 1259-1271.doi: 10.1016/S0252-9602(11)60313-5

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THE POINTWISE ESTIMATES TO SOLUTIONS FOR 1-DIMENSIONAL LINEAR THERMO-VISCO-ELASTIC SYSTEM

郝兴文1, 彭少玉2   

  1. 1.Mathematics Department, Shanghai Jiaotong University, Shanghai 200240, China, School of Mathematics and Information Sciences, Weifang University, Weifang 261061, China|2.School of Mathematics and Information, Ludong University, Yantai 264000, China
  • 收稿日期:2010-03-16 出版日期:2011-07-20 发布日期:2011-07-20
  • 基金资助:

    Xingwen Hao’s research was supported in part by National Natural Science Foundation of China (10571120 and 10971135), Shanghai Shuguang Project (06SG11) and the Program for New Century Excellent Talents of Chinese Ministry of Education (NCET-07-0546) and Doctorial Foundation of Weifang University (2011BS11).

THE POINTWISE ESTIMATES TO SOLUTIONS FOR 1-DIMENSIONAL LINEAR THERMO-VISCO-ELASTIC SYSTEM

 HAO Xin-Wen1, PENG Shao-Yu2   

  1. 1.Mathematics Department, Shanghai Jiaotong University, Shanghai 200240, China, School of Mathematics and Information Sciences, Weifang University, Weifang 261061, China|2.School of Mathematics and Information, Ludong University, Yantai 264000, China
  • Received:2010-03-16 Online:2011-07-20 Published:2011-07-20
  • Supported by:

    Xingwen Hao’s research was supported in part by National Natural Science Foundation of China (10571120 and 10971135), Shanghai Shuguang Project (06SG11) and the Program for New Century Excellent Talents of Chinese Ministry of Education (NCET-07-0546) and Doctorial Foundation of Weifang University (2011BS11).

摘要:

In this paper, we study the linear thermo-visco-elastic system in one-dimensional space variable. The mathematical model is a hyperbolic-parabolic partial differential sys- tem. The solutions of the system show some decay property due to the parabolicity. Based
on detailed analysis on the Green function of the system, the pointwise estimates of the solutions are obtained, from which the generalized Huygens’principle is shown.

关键词: thermo-visco-elastic system, Fourier transform, Green function, pointwise estimate, Huygens’principle

Abstract:

In this paper, we study the linear thermo-visco-elastic system in one-dimensional space variable. The mathematical model is a hyperbolic-parabolic partial differential sys- tem. The solutions of the system show some decay property due to the parabolicity. Based
on detailed analysis on the Green function of the system, the pointwise estimates of the solutions are obtained, from which the generalized Huygens’principle is shown.

Key words: thermo-visco-elastic system, Fourier transform, Green function, pointwise estimate, Huygens’principle

中图分类号: 

  • 53A08