论文标题
辐射传输方程的全球Lipschitz稳定性
Global Lipschitz stability for inverse problems for radiative transport equations
论文作者
论文摘要
我们考虑通过卡尔曼估计来确定辐射传输方程中源项的系数或时间独立因素的反面问题。我们建立了具有额外条件的全球Lipschitz稳定性结果，需要对初始值或给定的来源进行一些严格的积极性，但是与Machida和Yamamoto的现有工作相比，我们不需要在速度领域上进行任何额外的条件，这是本文的主要成就（{\ {\ IT逆问题} {\ bf 30} {\ bf 30} {\ bf 30} 03501010，2014年）。该证明依赖于Carleman估计值，并根据速度域的分区具有分段线性重量函数。
We consider inverse problems of determining coefficients or time independent factors of source terms in radiative transport equations by means of Carleman estimate. We establish global Lipschitz stability results with an additional condition which requires some strict positivity for initial value or given factor of source, but we need not any extra conditions on domains of velocities, which is the main achievement of this article compared with the existing work by Machida and Yamamoto ({\it Inverse Problems} {\bf 30} 035010, 2014). The proof relies on a Carleman estimate with a piecewise linear weight function according to the partition of the velocity domain.
