标题： 利用部分边界测量重构抛物方程的源函数 显示英文标题

标题： Reconstruction of source function in a parabolic equation using partial boundary measurements

摘要： 本文研究了利用部分边界测量值确定抛物型反源问题中依赖空间的源函数的优化方法的解析与数值解法。 给出了求解该优化问题的拉格朗日方法，并推导出最优性条件。 建立了正则化Tikhonov泛函Frechet可微性证明以及反源问题解的存在性结果。 还给出了未知源项的局部稳定性估计。 数值实例使用共轭梯度法（CGM）验证了二维和三维含噪声数据情况下的理论分析。 显示英文摘要

摘要： In this paper, we present the analytical and numerical study of the optimization approach for determining the space-dependent source function in the parabolic inverse source problem using partial boundary measurements. The Lagrangian approach for the solution of the optimization problem is presented, and optimality conditions are derived. The proof of the Fréchet differentiability of the regularized Tikhonov functional and the existence result for the solution of the inverse source problem are established. A local stability estimate for the unknown source term is also presented. The numerical examples justify the theoretical investigations using the conjugate gradient method (CGM) in 2D and 3D tests with noisy data.