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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…
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…
To address the ill-posedness of the inverse source problem for the one-dimensional stochastic Helmholtz equations without attenuation, this study develops a novel computational framework designed to mitigate this inherent challenge at the…
We improve the preceding results obtained by the first and the second authors in [3]. They concern the stability issue of the inverse problem that consists in determining the potential and the damping coefficient in a wave equation from an…
Numerically solving the 2D Helmholtz equation is widely known to be very difficult largely due to its highly oscillatory solution, which brings about the pollution effect. A very fine mesh size is necessary to deal with a large wavenumber…
This paper studies an inverse hyperbolic problem for the wave equation with dynamic boundary conditions. It consists of determining some forcing terms from the final overdetermination of the displacement. First, the Fr\'echet…
The problem of recovering acoustic sources, more specifically monopoles, from point-wise measurements of the corresponding acoustic pressure at a limited number of frequencies is addressed. To this purpose, a family of sparse optimization…
We consider increasing stability in the inverse Schr\"{o}dinger potential problem with power type nonlinearities at a large wavenumber. Two linearization approaches, with respect to small boundary data and small potential function, are…
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…
This article considers a Cauchy problem of Helmholtz equations whose solution is well known to be exponentially unstable with respect to the inputs. In the framework of variational quasi-reversibility method, a Fourier truncation is applied…
In this paper, we study for the first time the stability of the inverse source problem for the biharmonic operator with a compactly supported potential in $\mathbb R^3$. Firstly, to connect the boundary data with the unknown source, we…
This paper addresses a factorization method for imaging the support of a wave-number-dependent source function from multi-frequency data measured at a finite pair of symmetric receivers in opposite directions. The source function is given…
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…
A new numerical method to solve an inverse source problem for the Helmholtz equation in inhomogenous media is proposed. This method reduces the original inverse problem to a boundary value problem for a coupled system of elliptic PDEs, in…
We establish a link between stability estimates for a hyperbolic inverse problem via the Boundary Control method and the blowup of a constant appearing in the contexts of optimal unique continuation and cost of approximate controllability.
In this article, we discuss quantitative Runge approximation properties for the acoustic Helmholtz equation and prove stability improvement results in the high frequency limit for an associated partial data inverse problem modelled on…
This paper reports a breakdown in linear stability theory under conditions of neutral stability that is deduced by an examination of exponential modes of the form $h\approx {{e}^{i(kx-\omega t)}}$, where $h$ is a response to a disturbance,…
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…
This article addresses the inverse problem of simultaneously recovering both the wave speed coefficient and an unknown initial condition (acting as the source) for the multidimensional wave equation from a single passive boundary…
This paper deals with an inverse source problem for the $1$D time-fractional diffusion equation by using boundary measurement. The conditional stability in identification of the unknown source term is proved on the basis of the Fourier…