论文标题
真正的主要类型操作员的逆问题
Inverse problems for real principal type operators
论文作者
论文摘要
我们考虑一般真实主要类型差异操作员的逆边界价值问题。第一个结果指出，凯奇数据集唯一地确定了操作员的散射关系和较低系数的双分射线变换。我们还为普通运营商提供了两种不同的边界确定方法，并证明了确定非线性实际主类型方程系数的全局唯一性结果。本文提出了一种统一的方法，用于处理运输和波动方程的逆边界问题，并突出了奇点在相关逆问题解决方案中的传播作用。
We consider inverse boundary value problems for general real principal type differential operators. The first results state that the Cauchy data set uniquely determines the scattering relation of the operator and bicharacteristic ray transforms of lower order coefficients. We also give two different boundary determination methods for general operators, and prove global uniqueness results for determining coefficients in nonlinear real principal type equations. The article presents a unified approach for treating inverse boundary problems for transport and wave equations, and highlights the role of propagation of singularities in the solution of related inverse problems.
