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A major problem in solving multi-waves inverse problems is the presence of critical points where the collected data completely vanishes. The set of these critical points depend on the choice of the boundary conditions, and can be directly…
This paper establishes Lipschitz stability for the simultaneous recovery of a variable density coefficient and the initial displacement in a damped biharmonic wave equation. The data consist of the boundary Cauchy data for the Laplacian of…
This paper is mainly concerned with the inverse scattering problem of determining the unknown potential for the classical Schr\"odinger equation in two and three dimensions. We establish the increasing stability of the inverse scattering…
In this paper, we study an inverse problem for linear parabolic system with variable diffusion coefficients subject to dynamic boundary conditions. We prove a global Lipschitz stability for the inverse problem involving a simultaneous…
We propose a method to reconstruct the electrical current density from acoustically-modulated boundary measurements of time-harmonic electromagnetic fields. We show that the current can be uniquely reconstructed with Lipschitz stability. We…
We consider the multi-frequency inverse source problem in the presence of a non-homogeneous medium using passive measurements. Precisely, we derive stability estimates for determining the source from the knowledge of only the imaginary part…
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…
This paper is devoted to the inverse problem of determining the spatially dependent source in a time fractional diffusion-wave equation, with the aid of extra measurement data at subboundary. Uniqueness result is obtained by using the…
We study the inverse boundary value problem for the Helmholtz equation using the Dirichlet-to-Neumann map at selected frequencies as the data. A conditional Lipschitz stability estimate for the inverse problem holds in the case of…
In this paper, we study the phenomenon of increasing stability in the inverse boundary value problems for the biharmonic equation. By considering a linearized form, we obtain an increasing Lipschitz-like stability when k is large.…
This work considers a nonlinear inverse source problem in a coupled diffusion equation from the terminal observation. Theoretically, under some conditions on problem data, we build the uniqueness theorem for this inverse problem and show…
This paper is concerned with the inverse problem to recover the scalar, complex-valued refractive index of a medium from measurements of scattered time-harmonic electromagnetic waves at a fixed frequency. The main results are two…
The solution of a multi-frequency 1d inverse medium problem consists of recovering the refractive index of a medium from measurements of the scattered waves for multiple frequencies. In this paper, rigorous stability estimates are derived…
In this work, we investigate the stability issue of the inverse problem of determining the locations and time-dependent amplitudes of point sources in a parabolic equation with a non-self adjoint elliptic operator from boundary…
We consider the inverse source problem of determining a source term depending on both time and space variable for fractional and classical diffusion equations in a cylindrical domain from boundary measurements. With suitable boundary…
In this paper, we present a refined approach to establish a global Lipschitz stability for an inverse source problem concerning the determination of forcing terms in the wave equation with mixed boundary conditions. It consists of boundary…
We consider inverse problems for the first and half order time fractional equation. We establish the stability estimates of Lipschitz type in inverse source and inverse coefficient problems by means of the Carleman estimates.
Using uniform global Carleman estimates for discrete elliptic and semi-discrete hyperbolic equations, we study Lipschitz and logarithmic stability for the inverse problem of recovering a potential in a semi-discrete wave equation,…
Starting with far field data of time-harmonic acoustic or electromagnetic waves radiated by a collection of compactly supported sources in two-dimensional free space, we develop criteria and algorithms for the recovery of the far field…
We study stability aspects for the determination of space and time-dependent lower order perturbations of the wave operator in three space dimensions with point sources. The problems under consideration here are formally determined and we…