【摘要】 考虑在终端值已知的前提下重构二阶抛物型方程系数的反问题,此类反问题在许多应用科学领域具有重要意义.基于最优控制框架下,建立了控制泛函极小元的存在性和所满足的必要条件,并证明了相应的逼近解收敛于原问题的最优解.更多还原

【Abstract】 An inverse problem of identifying the coefficient of the parabolic equation is studied when the final observation is given.Such a problem has important application in large areas of applied science.Based on the optimal control framework,the existence and necessary condition of the minimizer for the control functional are established.It is proved that the corresponding approximate solutions converge to the optimal solution for the original problem.更多还原