‎in this paper‎, ‎we consider an inverse boundary value problem for two-dimensional heat equation in an annular domain‎. ‎this problem consists of determining the temperature on the interior boundary curve from the cauchy data (boundary temperature and heat flux) on the exterior boundary curve‎. ‎to this end‎, ‎the boundary integral equation method is used‎. ‎since the resulting system of linea...

In this paper, a nonlinear inverse problem of parabolic type, is considered. By reducing this inverse problem to a system of Volterra integral equations the existence, uniqueness, and stability of the solution will be shown.

A simple methodology that enables exact sensitivity analysis with unstructured meshes is presented. Using automatic differentiation, derivatives of highly non-linear state equations and cost functionals can be computed up to numerical precision. But with unstructured meshes, the nodal sensitivities, which are needed to perform the differentiation with respect to shape of the computational domai...

This study is set in the framework of inverse scattering of scalar (e.g. acoustic) waves. A qualitative probing technique based on the distribution of topological sensitivity of the cost functional associated with the inverse problem with respect to the nucleation of an infinitesimally-small hard obstacle is formulated. The sensitivity distribution is expressed as a bilinear formula involving t...

on a special interval. We obtain some nodal parameters like nodal points and nodal lengths. In addition, we reconstruct the potential function by nodal points. Results obtained in this paper are similar to the classical Sturm–Liouville problem. However, equations of this type are considered with the condition defined at the origin. We solve the problem on the interval [1,a], that problem is not...

In this paper we introduce a special form of symmetric matrices that is called central symmetric $X$-form matrix and study some properties, the inverse eigenvalue problem and inverse singular value problem for these matrices.

Inverse nodal problems are studied for second-order differential operators on graphs with a cycle and with standard matching conditions in the internal vertex. Uniqueness theorems are proved, and a constructive procedure for the solution is provided.

We consider network topology identification subject to a signal smoothness prior on the nodal observations. A fast dual-based proximal gradient algorithm is developed efficiently tackle strongly convex, smoothness-regularized inverse problem known yield high-quality graph solutions. Unlike existing solvers, novel iterations come with global convergence rate guarantees and do not require additio...