稳态扩散问题中Tikhonov正则化系数的收敛率

Convergence rates for Tikhonov regularization of coefficient identification in steady-state diffusion problems

摘要: 主要研究稳态扩散方程混合边值问题中未知传导系数的识别. 假设传导系数\alpha(x)未知，则由测量数据z^\delta=u(x), x\in\Omega可以唯一确定\alpha(x).此外, 在简化的来源条件下, 利用Tikhonov正则化方法, 可以得到扩散方程正则化解以及正则化传导系数的收敛率.

Abstract: A steady-state diffusion equation with mixed boundary values is investigated. If the conductivity \alpha(x) is unknown, with the measured data z^\delta=u(x) in \Omega, the \alpha(x) can be uniquely determined. In addition, under a simple source condition, the convergence rates for the regularized solutions and approximate conductivity are achieved.