基于积分观测条件反演退化抛物型方程的辐射系数  

Reconstructing the Radiative Coefficient for a Degenerate Parabolic Equation Based on Integral Observation Condition

作　　者：温鑫亮 WEN Xinliang(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：《重庆理工大学学报（自然科学）》2020年第10期238-246,共9页Journal of Chongqing University of Technology：Natural Science

基　　金：国家自然科学基金项目(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项目(18JR3RA122)。

摘　　要：研究了一类基于积分型观测条件重构二阶退化抛物型方程辐射系数的反问题,这类辐射系数仅依赖于空间变量,与其他类不同之处在于模型中的二阶项系数在边界处可退化为零。首先在弱弱退化条件下证明了原问题解的唯一性;由于原问题是不适定的,于是将原问题转化为一个优化问题,进而证明了极小元的存在性及其满足的必要条件,证明了极小元的稳定性和唯一性。Inverse problem of reconstructing the radiation coefficients of second order degenerate parabolic equation based on integral observation conditions is studied,and theradiative coefficient only depends on space variable.The difference from other work is that the second order coefficients in the model can degenerate to zero at the boundary.Firstly,the uniqueness of the solution of the original problem is proved under weakly degenerate conditions.Since the original problem is not well posed,the original problem is transformed into an optimization problem,theexistence and the necessary condition of the minimal element are established.Finally,we prove the stability and uniqueness of the minimal element.

关 键 词：反问题 辐射系数 退化抛物型方程 唯一性 最优控制 

分 类 号：O175.26[理学—数学]