重构非线性热传导方程导热系数的反问题  

The Inverse Problem of Reconstructing Thermal Conductivity of Nonlinear Heat Conduction Equation

作　　者：杨涛 解金鑫 温鑫亮 刘翻丽 YANG Tao;XIE Jin-xin;WEN Xin-liang;LIU Fan-li(School of Mathematics and Physics,Lanzhou Jiaotong University,Lanzhou 730070,China)

机构地区：[1]兰州交通大学数理学院

出　　处：《兰州交通大学学报》2019年第6期120-124,131,共6页Journal of Lanzhou Jiaotong University

基　　金：国家自然科学基金(11461039,61663018);兰州交通大学“百名青年优秀人才培养计划”;甘肃省自然科学基金(18JR3RA122)

摘　　要：研究了一个利用终端数据重构非线性热传导方程导热系数的反问题.首先利用有限体积法,得到了方程的差分格式,并证明了差分格式的稳定性.其次,利用有限差分格式得到了正问题的数值解.最后,通过Gradient型迭代方法对未知导热系数进行了数值模拟,数值结果表明未知导热系数重构的效果很好.An inverse problem of the thermal conductivity of a nonlinear heat conduction equation reconstructed from terminal data is studied.Firstly,the difference format of the equation is obtained by using the finite volume method,and the stability of the difference scheme is proved.Secondly,the positive problem is obtained by using the finite difference scheme.Finally,the unknown thermal conductivity is numerically simulated by the gradient type iterative method.The numerical results show that the unknown thermal conductivity reconstruction is very effective.

关 键 词：反问题 导热系数 Gradient型迭代 差分格式 稳定性 

分 类 号：O175.26[理学—数学]