A logarithmic estimate for inverse source scattering problem with attenuation in a two-layered medium

Linearized inverse Schrödinger potential problem at a large wavenumber

We investigate recovery of the (Schrödinger) potential function from many boundary measurements at a large wavenumber. By considering such a linearized form, we obtain a Hölder type stability which is a big improvement over a logarithmic stability in low wavenumbers. Furthermore we extend the discussion to the linearized inverse Schrödinger potential problem with attenuation, where an exponential dependence of the attenuation constant is traced in the stability estimate. Based on the linearized problem, a reconstruction algorithm is proposed aiming at the recovery of the Fourier modes of the p…

CTA流形上抛物型反问题的双对数稳定性

Double-logarithmic stability for a parabolic inverse problem on CTA manifolds

该论文在共形横截各向异性流形上，针对抛物型方程中时间相关势的反演问题，建立了双对数稳定性估计，通过部分输入-输出映射和均匀稳定性假设，结合高斯束拟模与Carleman估计等方法，证明了恢复的稳定性。