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:摘要:本文研究了辐射输运方程系数反演问题。开发了一种全局收敛的数值方法,即所谓的凸化方法。首次考虑了针对结果为两个偏微分方程的边值问题的粘性解。使用Laplace算子的Carleman估计证明了该边值问题的Lipschitz稳定性估计。随后,通过该Carleman估计提供了全局收敛分析。数值实验结果表明,该方法具有很高的计算效率。