An inverse problem of radiative potentials and initial temperatures in parabolic equations with dynamic boundary conditions

We study an inverse problem involving the restoration of two radiative potentials, not necessarily smooth, simultaneously with initial temperatures in parabolic equations with dynamic boundary conditions. We prove a Lipschitz stability estimate for the relevant potentials using a recent Carleman estimate, and a logarithmic stability result for the initial temperatures by a logarithmic convexity method, based on observations in an arbitrary subdomain.

Stability estimates for reconstruction from the Fourier transform on the ball

We prove Hölder-logarithmic stability estimates for the problem of finding an integrable function v on {{\mathbb{R}}^{d}} with a super-exponential decay at infinity from its Fourier transform {\mathcal{F}v} given on the ball {B_{r}}. These estimates arise from a Hölder-stable extrapolation of {\mathcal{F}v} from {B_{r}} to a larger ball. We also present instability examples showing an optimality of our results.

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

The paper aims a logarithmic stability estimate for the inverse source problem of the one-dimensional Helmholtz equation with attenuation factor in a two layer medium. We establish a stability by using multiple frequencies at the two end points of the domain which contains the compact support of the source functions.

NEW GLOBAL LOGARITHMIC STABILITY RESULTS ON THE CAUCHY PROBLEM FOR ELLIPTIC EQUATIONS

We prove the global logarithmic stability of the Cauchy problem for $H^{2}$-solutions of an anisotropic elliptic equation in a Lipschitz domain. The result is based on existing techniques used to establish stability estimates for the Cauchy problem combined with related tools used to study an inverse medium problem.