We shall study in this paper the Lipschitz type stabilities and convergence rates of Tikhonov regularization for the recovery of the radiativities in elliptic and parabolic systems with Dirichlet boundary conditions. The Lipschitz type stability estimates are derived. Due to the difficulty of the verification of the existing source conditions or nonlinearity conditions for the considered inverse radiativity problems in high dimensional spaces, some new variational source conditions are proposed. The conditions are rigorously verified in general dimensional spaces under the Lipschitz type stability estimates and the reasonable convergence rates are achieved.

中文翻译：

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椭圆和抛物线逆辐射问题的 Tikhonov 正则化的收敛率

我们将在本文中研究用于恢复具有狄利克雷边界条件的椭圆和抛物线系统中的辐射率的 Tikhonov 正则化的 Lipschitz 型稳定性和收敛速度。导出 Lipschitz 型稳定性估计值。由于高维空间中考虑的逆辐射性问题的现有源条件或非线性条件难以验证，提出了一些新的变分源条件。这些条件在 Lipschitz 型稳定性估计下的一般维空间中得到了严格验证，并获得了合理的收敛速度。