Related papers: Uniqueness and stability for inverse source proble…
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…
In this paper, the existence, uniqueness and dependence on initial value of solution for a singular diffusion equation with nonlinear boundary condition are discussed. It is proved that there exists a unique global smooth solution which…
In this article, we study the stability in the inverse problem of determining the time-dependent convection term and density coefficient appearing in the convection-diffusion equation, from partial boundary measurements. For dimension…
A new solution to the mono-dimensional diffusion equation for time-variable first kind boundary condition is presented where the time-variable function at the surface is derived proposing a surface saturation model. This solution may be…
We examine initial-boundary value problems for diffusion equations with distributed order time-fractional derivatives. We prove existence and uniqueness results for the weak solution to these systems, together with its continuous dependency…
The linearization principle states that the stability (or instability) of solutions to a suitable linearization of a nonlinear problem implies the stability (or instability) of solutions to the original nonlinear problem. In this work, we…
In this work we consider the computational approximation of a unique continuation problem for the Helmholtz equation using a stabilized finite element method. First conditional stability estimates are derived for which, under a convexity…
This paper considers the inverse problem of recovering state-dependent source terms in a reaction-diffusion system from overposed data consisting of the values of the state variables either at a fixed finite time (census-type data) or a…
Our aim is to study the backward problem, i.e. recover the initial data from the terminal observation, of the subdiffusion with time dependent coefficients. First of all, by using the smoothing property of solution operators and a…
Inverse problem to recover simultaneously a scalar coefficient, order of a time-fractional derivative, parameters of multiterm fractional Laplacian and a time-dependent source term occurring in a superdiffusion equation from measurements…
Inverse problems of recovering space-dependent parameters, e.g., initial condition, space-dependent source or potential coefficient, in a subdiffusion model from the terminal observation have been extensively studied in recent years.…
In this paper, we prove a uniqueness result in the inverse problem of determining several non-constant coefficients of one-dimensional reaction-diffusion equations. Such reaction-diffusion equations include the classical model of…
We address the inverse problem of identifying a time-dependent potential coefficient in a one-dimensional diffusion equation subject to Dirichlet boundary conditions and a nonlocal integral overdetermination constraint reflecting spatially…
This paper is concerning the inverse conductive scattering of acoustic waves by a bounded inhomogeneous object with possibly embedded obstacles inside. A new uniqueness theorem is proved that the conductive object is uniquely determined by…
This paper is concerned with the inverse random source problem for a stochastic time fractional diffusion equation, where the source is assumed to be driven by a Gaussian random field. The direct problem is shown to be well-posed by…
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…
In this work we develop a new numerical approach for recovering a spatially dependent source component in a standard parabolic equation from partial interior measurements. We establish novel conditional Lipschitz stability and H\"{o}lder…
This paper is concerned with the uniqueness in inverse acoustic scattering problems with the modulus of the far-field patterns co-produced by the obstacle (resp. medium) and the point sources. Based on the superposition of point sources as…
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…
This paper is concerned with the inverse problem to recover the scalar, complex-valued refractive index of a medium from measurements of scattered time-harmonic electromagnetic waves at a fixed frequency. The main results are two…