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系数反问题，提出了全局收敛数值方法——即所谓的凸化方法。首次针对所得两个耦合偏微分方程系统的边值问题引入粘性解。利用拉普拉斯算子的Carleman估计，证明了该边值问题的Lipschitz稳定性估计。随后，基于该Carleman估计给出了全局收敛性分析。数值实验结果表明该方法具有较高的计算效率。