In this paper, an inverse nodal problem for a second-order differential equation having a chemical potential on a finite interval is investigated. First, we estimate the nodal points and nodal lengths of differential operator. Then, we show that the potential can be uniquely determined by a dense set of nodes of the eigenfunctions.

We consider the inverse problem of determining the shape of some inaccessible portion of the boundary of a region in n dimensions from Cauchy data for the heat equation on an accessible portion of the boundary. The inverse problem is quite ill-posed, and nonlinear. We develop a Newton-like algorithm for solving the problem, with a simple and efficient means for computing the required derivative...

We establish a Lipschitz stability estimate for the inverse problem consisting in the determination of the coe cient σ(t), appearing in a Dirichlet initial-boundary value problem for the parabolic equation ∂tu − ∆xu + σ(t)f(x)u = 0, from Neumann boundary data. We extend this result to the same inverse problem when the previous linear parabolic equation is changed to the semi-linear parabolic eq...

In this work, we tried to find the inverse coefficient in the Euler problem with over determination conditions. It showed the existence, stability of the solution by iteration method and linearization method was used for this problem in numerical part. Also two examples are presented with figures.

We consider the inverse problem of determining the shape of some inaccessible portion of the boundary of a region in n dimensions from Cauchy data for the heat equation on an accessible portion of the boundary. The inverse problem is quite ill-posed, and nonlinear. We develop a Newton-like algorithm for solving the problem, with a simple and efficient means for computing the required derivative...

The interior transmission problem is a boundary value problem that plays a basic role in inverse scattering theory but unfortunately does not seem to be included in any existing theory in partial differential equations.This paper presents old and new results for the interior transmission problem ,in particular its relation to inverse scattering theory and new results on the spectral theory asso...

We report on the results of an EIT phantom study using an experimental tank with agar conductivity inhomogeneities, used to verify the accuracy of both a boundary element method (BEM) forward model and a non-linear inverse solution based on the BEM model. We introduce the shunt electrode model into the BEM equations for greater accuracy and derive the associated Jacobian for the inverse problem...

Electrical Capacitance Tomography is an ill-posed inverse problem that aims at recovering the spatial permittivity distribution of an inhomogeneous medium from capacitance measurements at the boundary. We consider the problem of fast robust estimation of inclusion shape and position in binary mixtures. The boundary of the inclusion is represented implicitly using a radial basis function represe...

We prove a Carleman estimate and a logarithmic stability estimate for an inverse problem in three dimensional viscoelasticity. More precisely, we obtain logarithmic stability for the inverse problem of recovering the spatial part of a viscoelastic coefficient of the form p(x)h(t) from a unique measurement on an arbitrary part of the boundary. The main assumptions are: h′(0) = 0, h(0) 6= 0, p is...