退化抛物型方程的一个源项反演问题  

A Source Term Inversion Problem for Degenerate Parabolic Equations

作　　者：马鑫 MA Xin(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,甘肃兰州730070

出　　处：《新乡学院学报》2024年第12期17-23,共7页Journal of Xinxiang University

基　　金：国家自然科学基金资助项目(61663018,11961042);甘肃省自然科学基金资助项目(22JR5RA341)。

摘　　要：在利用终端观测温度重构退化热传导方程中,研究了空间依赖热源的反问题。以最优控制框架为基础,将反问题转化为优化问题,证明了目标泛函极小值的存在的必要条件。提出了一种构造二阶精度差分格式的方法,利用共轭梯度法求出了反问题的数值解,提高了算法收敛速度。数值实验结果表明,所设计的算法具有较高的反演效率和稳定性,对未知热源进行重构时能取得较好的效果。In reconstructing the degraded heat conduction equation by using terminal temperature observations,the inverse problem of spatially dependent heat sources is studied.The inverse problem is transformed into an optimization problem based on the optimal control framework,the necessary condition for the existence of the minimum value of the objective functional is proved.A method for constructing a second-order precision difference scheme is proposed,and the numerical solution of the inverse problem is obtained by the conjugate gradient method,which improved the convergence speed of the algorithm.The numerical experimental results indicate that the designed algorithm has high inversion efficiency and stability,and can achieve good results in reconstructing unknown heat sources.

关 键 词：退化抛物型方程 反热源问题 最优控制 共轭梯度法 数值结果 

分 类 号：O241.82[理学—计算数学]