李景, 郭柏灵. 稳态扩散问题中Tikhonov正则化系数的收敛率[J]. 华南师范大学学报(自然科学版), 2013, 45(2).
引用本文: 李景, 郭柏灵. 稳态扩散问题中Tikhonov正则化系数的收敛率[J]. 华南师范大学学报(自然科学版), 2013, 45(2).
Convergence rates for Tikhonov regularization of coefficient identification in steady-state diffusion problems[J]. Journal of South China Normal University (Natural Science Edition), 2013, 45(2).
Citation: Convergence rates for Tikhonov regularization of coefficient identification in steady-state diffusion problems[J]. Journal of South China Normal University (Natural Science Edition), 2013, 45(2).

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.

     

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