Related papers: An Inverse Problem for the Relativistic Boltzmann …
We propose a numerical method to solve an inverse source problem of computing the initial condition of hyperbolic equations from the measurements of Cauchy data. This problem arises in thermo- and photo- acoustic tomography in a bounded…
This article is concerned with the inverse problem on determining the temporal component of the source term in a coupled system of time-fractional diffusion equations by single point observation. Under a non-degeneracy condition on the…
We initiate the study of inverse source problems for quasilinear elliptic equations of the form \[ \left\{ \begin{array}{ll} \nabla \cdot (\gamma(x,u,\nabla u) \nabla u) = F & \text{in } \Omega, \\ u = f & \text{on } \partial\Omega,…
In this article, we study an inverse problem consisting in the identification of a space-time dependent source term in the Ginzburg-Landau equation from final-time observations. We adopt a weak-solution framework and analyze Tikhonov's…
The notion of distance between a global Maxwellian function and an arbitrary solution $f$ (with the same total density $\rho$ at the fixed moment $t$) of Boltzmann equation is introduced. In this way we essentially generalize the important…
In this paper, we investigate an inverse random source problem concerned with recovering the strength of a random, uncorrelated acoustic source from correlation measurements of emitted time-harmonic acoustic waves. Such problems arise in…
In this paper, we investigate the inverse problem of determining the right-hand side of a subdiffusion equation with a Caputo time derivative, where the right-hand side depends on both time and certain spatial variables. Similar inverse…
This work studies the inverse problem of photoacoustic tomography (more precisely, the acoustic subproblem) as the identification of a space-dependent source parameter. The model consists of a wave equation involving a time-fractional…
In this paper, we study two types of inverse problems for space semi-discrete stochastic parabolic equations in arbitrary dimensions. The first problem concerns a semi-discrete inverse source problem, which involves determining the random…
This work investigates an inverse problem of determining the radiative coefficient in a degenerate parabolic equation from the final overspecified data. Being different from other inverse coefficient problems in which the principle…
In the context of optimal control, we consider the inverse problem of Lagrangian identification given system dynamics and optimal trajectories. Many of its theoretical and practical aspects are still open. Potential applications are very…
This article is devoted to inverse problems of recovering point sources in mathematical models of heat and mass transfer. The main attention is paid to well-posedness questions of these inverse problems with pointwise overdetermination…
For the first time, we develop in this paper the globally convergent convexification numerical method for a Coefficient Inverse Problem for the 3D Helmholtz equation for the case when the backscattering data are generated by a point source…
In this paper we investigate the Bayesian approach to inverse Robin problems. These are problems for certain elliptic boundary value problems of determining a Robin coefficient on a hidden part of the boundary from Cauchy data on the…
This paper is concerned with inverse acoustic source problems in an unbounded domain with dynamical boundary surface data of Dirichlet kind. The measurement data are taken at a surface far away from the source support. We prove uniqueness…
Inverse scattering problems have many important applications. In this paper, given limited aperture data, we propose a Bayesian method for the inverse acoustic scattering to reconstruct the shape of an obstacle. The inverse problem is…
We consider the inverse problem to determine a smooth compact Riemannian manifold with boundary $(M, g)$ from a restriction $\Lambda_{\Src, \Rec}$ of the Dirichlet-to-Neumann operator for the wave equation on the manifold. Here $\Src$ and…
We start with some global Maxwellian function $M$, which is a stationary solution (with the constant total density $\rho$) of the Boltzmann equation, and we denote the number of the corresponding space variables by $n$. The notion of…
The paper is devoted to the development of the theory of inverse problems for evolution equations with terms rapidly oscillating in time. A new approach to setting such problems is developed for the case in which additional constraints are…
We consider the formally determined inverse problem of recovering an unknown time-dependent potential function from the knowledge of the restriction of the solution of the wave equation to a small subset, subject to a single external…