稳态扩散问题中Tikhonov正则化系数的收敛率

基金项目:

国家青年自然科学基金;湖南省教育厅项目

详细信息

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.
- 不适定问题
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.
- Ill-posed problems