摘要
本文在 n 维区域Ω中考虑具有未知系数α(x)的抛物方程 u_t=α(x)△u.以解的终值条件为超定数据,利用 Banach 空间中算子的 Gateaux 导数及压缩映象原理,证明了反问题的解的唯一性和稳定性.
This paper gives consideration to the parabolic equation u_t=a(x)△u in an n-dimenslonal domain Ω,where spatially-dependent coefficient α(x) is unknow n.By the overspecified final data and Gateaux derivative of the operator in Banach space and image compression theorem,it is proved that this problem is stable in a sense,and then a uniqueness theorem.is given.
基金
高校科研基金资助课题
关键词
抛物方程
未知系数
反问题
parabolic equation
unknown coefficient
inverse problem
uniqueness
existence
