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We consider a strongly damped wave equation on compact manifolds, both with and without boundaries, and formulate the corresponding inverse problems. For closed manifolds, we prove that the metric can be uniquely determined, up to an…
We consider the inverse problem for the wave equation which consists of determining an unknown space-dependent force function acting on a vibrating structure from Cauchy boundary data. Since only boundary data are used as measurements, the…
We consider the inverse dynamic problem for the wave equation with a potential on a real line. The forward initial-boundary value problem is set up with a help of boundary triplets. As an inverse data we use an analog of a response operator…
We consider inverse problems of determining coefficients or time independent factors of source terms in radiative transport equations by means of Carleman estimate. We establish global Lipschitz stability results with an additional…
We investigate the propagation of infinitesimal harmonic mechanical waves emitted from a boundary with variable velocity and arriving at a stationary observer. In the classical Doppler effect, $X_\mathrm{s}(t) = vt$ is the location of the…
In this paper, we will study increasing stability in the inverse source problem for the Helmholtz equation in the plane when the source term is assumed to be compactly supported in a bounded domain $\Omega$ with sufficiently smooth…
We consider the inverse problem of determining different type of information about a diffusion process, described by ordinary or fractional diffusion equations stated on a bounded domain, like the density of the medium or the velocity field…
We consider point sources in hyperbolic equations discretized by finite differences. If the source is stationary, appropriate source discretization has been shown to preserve the accuracy of the finite difference method. Moving point…
This paper is about Holder and Lipschitz stability estimates and uniqueness theorems for some coefficient inverse problems and associated inverse source problems for a general linear parabolic equation of the second order with variable…
We establish both Lipschitz and logarithmic stability estimates for an inverse flux problem and subsequently apply these results to an inverse boundary coefficient problem. Furthermore, we demonstrate how the stability inequalities derived…
In this article we study inverse source problems for time-fractional diffusion equations from \textit{a posteriori} boundary measurement. Using the memory effect of these class of equations, we solve these inverse problems for several class…
This paper investigates an inverse random source problem for stochastic evolution equations, including stochastic heat and wave equations, with the unknown source modeled as $g(x)f(t)\dot{W}(t)$. The research commences with the…
We study an inverse problem for the wave equation, concerned with estimating the wave speed, aka velocity, from data gathered by an array of sources and receivers that emit probing signals and measure the resulting waves. The typical…
This paper is concerned with time domain forward scattering and inverse scattering problems with a single moving point source as the emitter. Approximate solutions are provided for the forward scattering problem with a moving emitter.…
In this work we investigate the inverse problem of recovering one point source in the heat equation from sparse boundary measurement, i.e., the flux data at several points on the boundary. We prove the unique recovery of the location and…
In this paper, we investigate a discrete inverse problem of determining three unknowns, i.e. initial displacement, initial velocity and random source term, in a fully discrete approximation of one-dimensional stochastic hyperbolic equation.…
We study the inverse problem for determining the time-dependent matrix potential appearing in the wave equation. We prove the unique determination of potential from the knowledge of solution measured on a part of the boundary.
This paper investigates an inverse source problem for space-time fractional diffusion equations from a posteriori interior measurements. The uniqueness result is established by the memory effect of fractional derivatives and the unique…
In this paper, we are concerned with the stochastic time-fractional diffusion-wave equations in a Hilbert space. The main objective of this paper is to establish properties of the stochastic weak solutions of the initial-boundary value…
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…