Related papers: Theoretical stability and numerical reconstruction…
We consider the multi-frequency inverse source problem for the scalar Helmholtz equation in the plane. The goal is to reconstruct the source term in the equation from measurements of the solution on a surface outside the support of the…
This paper considers the inverse problem of identifying the source term of parabolic equations from sparse boundary measurements. We used data from moving sensors to locate the unknown source term. This work first proves the uniqueness of…
We introduce in this document a direct method allowing to solve numerically inverse type problems for linear parabolic equations. We consider the reconstruction of the full solution of the parabolic equation posed in $\Omega\times (0,T)$ -…
In this paper, we study an inverse problem of identifying two spatial-temporal source terms in the Schr\"odinger equation with dynamic boundary conditions from the final time overdetermination. We adopt a weak solution approach to solve the…
This paper is concerned with an inverse wavenumber/frequency-dependent source problem for the Helmholtz equation. In two and three dimensions, the unknown source term is supposed to be compactly supported in spatial variables but…
A version of the convexification numerical method for a Coefficient Inverse Problem for a 1D hyperbolic PDE is presented. The data for this problem are generated by a single measurement event. This method converges globally. The most…
In this paper we consider the computation of approximate solutions for inverse problems in Hilbert spaces. In order to capture the special feature of solutions, non-smooth convex functions are introduced as penalty terms. By exploiting the…
In this paper, we investigate an ill-posed Cauchy problem involving a stochastic parabolic equation. We first establish a Carleman estimate for this equation. Leveraging this estimate, we derive the conditional stability and convergence…
This paper is concerned with the inverse scattering problem which aims to determine the spatially distributed dielectric constant coefficient of the 2D Helmholtz equation from multifrequency backscatter data associated with a single…
This paper is concerned with the stability estimates for inverse source problems of the stochastic Helmholtz equation driven by white noise. The well-posedness is established for the direct source problems, which ensures the existence and…
This paper is concerned with the stability of the inverse source problem for the damped biharmonic plate equation in three dimensions. The stability estimate consists of the Lipschitz type data discrepancy and the high frequency tail of the…
This paper concerns the inverse source problem for the time-harmonic wave equation in a one dimensional domain. The goal is to determine the source function from the boundary measurements. The problem is challenging due to complexity of the…
We consider the Cauchy problem and the source problem for normally hyperbolic operators on the Minkowski spacetime, and study the determination of solutions from their integrals along null geodesics. For the Cauchy problem, we give a new…
We study the stability in the inverse problem of determining the time dependent zeroth-order coefficient $q(t,x)$ arising in the wave equation, from boundary observations. We derive, in dimension $n\geq 2$, a log-type stability estimate in…
We consider a second-order hyperbolic equation on an open bounded domain $\Omega$ in $\mathbb{R}^n$ for $n\geq2$, with $C^2$-boundary $\Gamma=\pa\Omega=\bar{\Gamma_0\cup\Gamma_1}$, $\Gamma_0\cap\Gamma_1=\emptyset$, subject to…
For linearized Navier-Stokes equations, we consider an inverse source problem of determining a spatially varying divergence-free factor. We prove the global Lipschitz stability by interior data over a time interval and velocity field at…
In this paper, we show for the first time the increasing stability of the inverse source problem for the n-dimensional Helmholtz equation at multiple wave numbers, which is different from the two-or three-dimensional Helmholtz equation. In…
Conditional stability estimates require additional regularization for obtaining stable approximate solutions if the validity area of such estimates is not completely known. In this context, we consider ill-posed nonlinear inverse problems…
We study increasing stability in the inverse source problems for the Helmholtz equation and the classical Lame system from (minimal) boundary data at multiple wave numbers. By using the Fourier transform with respect to wave numbers,…
We study a non-linear statistical inverse learning problem, where we observe the noisy image of a quantity through a non-linear operator at some random design points. We consider the widely used Tikhonov regularization (or method of…