A Coefficient Inverse Problem for the radiative transport equation is considered. The globally convergent numerical method, the so-called convexification, is developed. For the first time, the viscosity solution is considered for a boundary value problem for the resulting system of two coupled partial differential equations. A Lipschitz stability estimate is proved for this boundary value problem using a Carleman estimate for the Laplace operator. Next, the global convergence analysis is provided via that Carleman estimate. Results of numerical experiments demonstrate a high computational efficiency of this approach.

翻译：考虑辐射传输方程的一个系数反问题。本文发展了一种全局收敛数值方法——即所谓的凸化方法。首次针对由两个耦合偏微分方程组成的系统的边界值问题引入粘性解概念。利用拉普拉斯算子的卡勒曼估计，证明了该边界值问题的利普希兹稳定性估计。进而通过该卡勒曼估计给出全局收敛性分析。数值实验结果表明该方法具有较高的计算效率。