Related papers: Parameter Reconstruction for general transport equ…
We consider the inverse problem of reconstructing the optical parameters of the radiative transfer equation (RTE) from boundary measurements in the diffusion limit. In the diffusive regime (the Knudsen number $\mathsf{Kn}\ll 1$), the…
We address the inverse problem of recovering a degeneracy point within the diffusion coefficient of a one-dimensional complex parabolic equation by observing the normal derivative at one point of the boundary. The strongly degenerate case…
We study the inverse boundary value problem for the Helmholtz equation using the Dirichlet-to-Neumann map at selected frequency as the data. We develop an explicit reconstruction of the wavespeed using a multi-level nonlinear projected…
A complete formulation is given of an exact kinetic theory for lattice gases. This kinetic theory makes possible the calculation of corrections to the usual Boltzmann / Chapman-Enskog analysis of lattice gases due to the buildup of…
We consider an inverse source problem for partially coherent light propagating in the Fresnel regime. The data is the coherence of the field measured away from the source. The reconstruction is based on a minimum residue formulation, which…
We study an inverse source problem for a semilinear parabolic equation in a bounded domain, where the nonlinearity depends on the unknown function and its gradient through a quadratic reaction term and a Burgers-type convection term. From…
We study an inverse problem involving the restoration of two radiative potentials, not necessarily smooth, simultaneously with initial temperatures in parabolic equations with dynamic boundary conditions. We prove a Lipschitz stability…
This paper is devoted to the inverse problem of recovering the unknown distributed flux on an inaccessible part of boundary using measurement data on the accessible part. We establish and verify a variational source condition for this…
In a medium where the dielectric permittivity is perturbed in the presence of an acoustic wave, optical scattering generates frequency-shifted light. In this paper we consider the inverse problem of recovering the optical properties of this…
This paper concerns about the weak unique continuation property of solutions of a general system of differential equation/inequality with a second order strongly elliptic system as its leading part. We put not only some natural assumption…
In this paper we consider the problem of recovering the conformal factor in a conformal class of Riemannian metrics from the boundary measurement of one wave field. More precisely, using boundary control operators, we derive an explicit…
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…
In this work, we consider an inverse problem of determining a source term for a structural acoustic partial differentia equation (PDE) model, comprised of a two or three-dimensional interior acoustic wave equation coupled to a Kirchoff…
This paper concerns the inverse problem of retrieving a stationary potential for the Schr\"odinger evolution equation in a bounded domain of RN with Dirichlet data and discontinuous principal coefficient a(x) from a single time-dependent…
In this work, we study the inverse problem of recovering a potential coefficient in the subdiffusion model, which involves a Djrbashian-Caputo derivative of order $\alpha\in(0,1)$ in time, from the terminal data. We prove that the inverse…
This paper presents an inverse problem for the nonlinear 1-d Kuramoto-Sivashinsky (K-S) equation. More precisely, we study the nonlinear inverse problem of retrieving the anti-diffusion coefficient from the measurements of the solution on a…
We consider an inverse problem of recovering the non-linearity in the one dimensional variable exponent $p(x)$-Laplace equation from the Dirichlet-to-Neumann map. The variable exponent can be recovered up to the natural obstruction of…
We consider the problem of reconstructing of the boundary of an unknown inclusion together with its conductivity from the localized Dirichlet-to-Neumann map. We give an exact reconstruction procedure and apply the method to an inverse…
In this paper, we present the analytical and numerical study of the optimization approach for determining the space-dependent source function in the parabolic inverse source problem using partial boundary measurements. The Lagrangian…
We consider an inverse source problem in the stationary radiative transport through an absorbing and scattering medium in two dimensions. Using the angularly resolved radiation measured on an arc of the boundary, we propose a numerical…