Related papers: Uniqueness and numerical reconstruction for invers…
The recovery of a spherically-symmetric wave speed $v$ is considered in a bounded spherical region of radius $b$ from the set of the corresponding transmission eigenvalues for which the corresponding eigenfunctions are also spherically…
We consider the inverse problem of quantitative reconstruction of properties (e.g., bulk modulus, density) of visco-acoustic materials based on measurements of responding waves after stimulation of the medium. Numerical reconstruction is…
We study an inverse problem for the viscoacoustic wave equation, an integro-differential model describing wave propagation in viscoacoustic media with memory in the leading order term. The medium is characterized by a spatially varying…
The inverse problem of finding the velocity profile from the surface measurements of acoustic field is considered. The dimensionalities of the data and of the unknown velocity profile are equal, both are equal 3. Analytical explicit…
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…
Under consideration are mathematical models of heat and mass transfer. We study inverse problems of recovering lower-order coefficients in a second order parabolic equation. The coefficients are representable in the form of a finite…
We study an inverse problem for the fractional wave equation with a potential by the measurement taking on arbitrary subsets of the exterior in the space-time domain. We are interested in the issues of uniqueness and stability estimate in…
An inverse source problem for the heat equation is considered. Extraction formulae for information about the time and location when and where the unknown source of the equation firstly appeared are given from a single lateral boundary…
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…
Our work concerns the study of inverse problems of heat and wave equations involving the fractional Laplacian operator with zeroth order nonlinear perturbations. We recover nonlinear terms in the semilinear equations from the knowledge of…
In this paper we consider the problem of simultaneously determining the time-dependent thermal diffusivity and the temperature distribution in one-dimensional heat equation in the case of nonlocal boundary and integral overdetermination…
The interval numbers is the set of compact intervals of $\mathbb{R}$ with addition and multiplication operation, which are very useful for solving calculations where there are intervals of error or uncertainty, however, it lacks 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…
This paper is devoted to the inverse problem of determining the spatially dependent source in a time fractional diffusion-wave equation, with the aid of extra measurement data at subboundary. Uniqueness result is obtained by using the…
We study the diffusion (or heat) equation on a finite 1-dimensional spatial domain, but we replace one of the boundary conditions with a "nonlocal condition", through which we specify a weighted average of the solution over the spatial…
In this paper we the formulation of inverse problems as constrained minimization problems and their iterative solution by gradient or Newton type. We carry out a convergence analysis in the sense of regularization methods and discuss…
This paper is concerned with the inverse problem of scattering of time-harmonic acoustic waves by an inhomogeneous penetrable obstacle in a piecewise homogeneous medium. The well-posedness of the direct problem is first established by using…
To numerically evolve the full Einstein equations (or modifications thereof), simulations of cosmological spacetimes must rely on a particular formulation of the field equations combined with a specific gauge/frame choice. Yet truly…
We consider fractional diffusion-wave equations with source term which is represented in a form of a product of a temporal function and a spatial function. We prove the uniqueness for inveres source problem of determining spatially varying…
In this article, we investigate inverse source problems for a wide range of PDEs of parabolic and hyperbolic types as well as time-fractional evolution equations by partial interior observation. Restricting the source terms to the form of…