退化抛物型方程源项系数识别反问题  

Inverse Problem of Source Term Coefficient Identificationfor Degenerate Parabolic Equation

作　　者：任如霞 REN Ru-xia(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：《兰州文理学院学报（自然科学版）》2021年第3期1-7,共7页Journal of Lanzhou University of Arts and Science(Natural Sciences)

基　　金：国家自然科学基金资助项目(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资助项目(18JR3RA122)。

摘　　要：利用最终测量温度,重构抛物型热方程中一个与空间相关的热源.在最优控制框架的基础上,将反问题转化为优化问题,并建立了代价泛函最小值的存在性和必要条件,最终由必要条件得到了最小值的全局唯一性和稳定性.A spatially dependent heat source in the parabolic heat equation was reconstructed by using the final measured temperature.Based on the optimal control framework,the inverse problem was transformed into an optimization problem,and the existence and necessary conditions of the minimum value of the cost functional were established.Finally,the global uniqueness and stability of the minimum value were obtained from the necessary conditions.

关 键 词：反问题 源项 最优控制 存在性 唯一性 稳定性 

分 类 号：O175.26[理学—数学]