相关论文: Uniqueness of time-dependent inclusions in anisotr…
We consider an inverse boundary value problem for the heat equation $\partial_t v = {\rm div}_x\,(\gamma\nabla_x v)$ in $(0,T)\times\Omega$, where $\Omega$ is a bounded domain of $R^3$, the heat conductivity $\gamma(t,x)$ admits a surface…
We study an inverse boundary value problem on the determination of principal order coefficients in isotropic nonautonomous heat flows stated as follows; given a medium, and in the absence of heat sources and sinks, can the time-dependent…
We discuss the inverse problem of determining the, possibly anisotropic, conductivity of a body $\Omega\subset\mathbb{R}^{n}$ when the so-called Neumann-to-Dirichlet map is locally given on a non empty curved portion $\Sigma$ of the…
We consider the inverse boundary value problem of recovering piecewise homogeneous elastic tensor and piecewise homogeneous mass density from a localized lateral Dirichlet-to-Neumann or Neumann-to-Dirichlet map for the elasticity equation…
This work deals with the problem of determining a non-homogeneous heat conductivity profile in a steady-state heat conduction boundary-value problem with mixed Dirichlet-Neumann boundary conditions over a bounded domain in $\mathbb{R}^n$,…
We consider initial boundary value problems for one-dimensional diffusion equation with time-fractional derivative of order $\alpha \in (0,1)$ which are subject to non-zero Neumann boundary conditions. We prove the uniqueness for an inverse…
We construct anisotropic conductivities with the same Dirichlet-to-Neumann map as a homogeneous isotropic conductivity. These conductivities are singular close to a surface inside the body.
In this article, we study an inverse boundary value problem for the time-dependent convection-diffusion equation. We use the nonlinear Carleman weight to recover the time-dependent convection term and time-dependent density coefficient…
The enclosure method was originally introduced for inverse problems of concerning non-destructive evaluation governed by elliptic equations. It was developed as one of useful approaches in inverse problems and applied for various equations.…
We investigate uniqueness in the inverse problem of reconstructing simultaneously a spacewise conductivity function and a heat source in the parabolic heat equation from the usual conditions of the direct problem and additional information…
Three inverse boundary value problems for the heat equations in one space dimension are considered. Those three problems are: extracting an unknown interface in a heat conductive material, an unknown boundary in a layered material or a…
We derive asymptotic expansions for the displacement at the boundary of a smooth, elastic body in the presence of small inhomogeneities. Both the body and the inclusions are allowed to be anisotropic. This work extends prior work of…
We discuss the inverse problem of determining the, possibly anisotropic, conductivity of a body $\Omega\subset\mathbb{R}^{n}$ when the so--called Dirichlet-to-Neumann map is locally given on a non empty portion $\Gamma$ of the boundary…
We study partial data inverse problems for linear and nonlinear parabolic equations with unknown time-dependent coefficients. In particular, we prove uniqueness results for partial data inverse problems for semilinear reaction-diffusion…
This paper studies a prototype of inverse initial boundary value problems whose governing equation is the heat equation in three dimensions. An unknown discontinuity embedded in a three-dimensional heat conductive body is considered. A {\it…
We study the inverse boundary value problem of detecting a non-uniform conductivity motivated by pacing-guided ablation in cardiac electrophysiology. At the stationary level, the transmembrane potential $u$ in a region…
A class of inverse problems for a heat equation with involution perturbation is considered using four different boundary conditions, namely, Dirichlet, Neumann, periodic and anti-periodic boundary conditions. Proved theorems on existence…
In this paper we study an inverse problem for fractional anisotropic conductivity. Our nonlocal operator is based on the well-developed theory of nonlocal vector calculus, and differs substantially from other generalizations of the…
We study inverse boundary problems for a one dimensional linear integro-differential equation of the Gurtin--Pipkin type with the Dirichlet-to-Neumann map as the inverse data. Under natural conditions on the kernel of the integral operator,…
In this article, we study the unique determination of convection term and the time-dependent density coefficient appearing in a convection-diffusion equation from partial Dirichlet to Neumann map measured on boundary.