论文标题
一阶双曲方程的逆问题，具有时间依赖的系数
Inverse problems for first-order hyperbolic equations with time-dependent coefficients
论文作者
论文摘要
我们证明了针对一阶线性双曲线方程的逆源和系数问题的全局Lipschitz稳定性，其系数均取决于空间和时间。我们使用了本文中引入的全球卡尔曼估计值，以及一个关键点是由双曲线操作员主要部分生成的向量场的积分曲线长度的选择，以构建卡尔曼估计的权重函数。在某些情况下，这些积分曲线对应于特征曲线。
We prove global Lipschitz stability for inverse source and coefficient problems for first-order linear hyperbolic equations, the coefficients of which depend on both space and time. We use a global Carleman estimate, and a crucial point, introduced in this paper, is the choice of the length of integral curves of a vector field generated by the principal part of the hyperbolic operator to construct a weight function for the Carleman estimate. These integral curves correspond to the characteristic curves in some cases.
