带积分型源项二阶拋物型方程的参数识别问题

An Inverse Problem of Identifying the Coefficient of Second Order Parabolic Equation with Integral Source Term

摘要: 本文主要研究的是带积分型源项二阶拋物型方程的参数识别问题，利用最优控制框架来建立控制泛函，并证明控制泛函极小元的存在性和必要条件，由于最优控制问题一般不存在唯一解，所以本文证明的是解的局部唯一性和稳定性。

Abstract: This paper mainly studies an inverse problem of identifying the coefficient of second order para-bolic equation with integral source term. We use the optimal control framework to establish control functional and prove the existence, and the necessary conditions of the minimum for the control functional are established. Since the optimal control problem is nonconvex, one may not expect a unique solution. However in this paper the solution is proved to be locally unique and stable.