<p style='text-indent:20px;'>In the present work we introduce and study a new method for solving inverse obstacle problem. It consists in identifying perfectly conducting inclusion <inline-formula><tex-math id="M1">\begin{document}$ \omega $\end{document}</tex-math></inline-formula> contained larger bounded domain id="M2">\begin{document}$ \Omega via boundary me...

This article considers an inverse problem of time fractional parabolic partial differential equations with the nonlocal boundary condition. Dirichlet-measured output data are used to distinguish unknown coefficient. A finite difference scheme is constructed and a numerical approximation made. Examples experiments, such as man-made noise, provided show stability efficiency this method.

We consider an inverse problem for a second order hyperbolic initial boundary value problem on a compact Riemannian manifold M with boundary. Assume that we know ∂M and the Cauchy data on ∂M × [0, T ] of the solutions with vanishing initial data. In the paper we consider two problems. Firstly, when T is sufficiently large and the Riemannian manifold satisfies an additional geometrical condition...

In this paper, we consider the inverse problem for the Laplace equation in two-dimensions which requires the determination of the location, size and shape of an unknown, or partially unknown, portion @ of the boundary @ of a solution domain R from additional Cauchy data on the remaining portion of the boundary 1⁄4 @ . This problem arises in the study of quantitative non-destructive evaluation o...

The task of the image reconstruction in Electrical Impedance Tomography (EIT) is highly ill-posed inverse problem. The level set method with the gradient technique is established model for our numerical problem. Interfaces between subdomains with constant conductivities are represented by the level set function. Moreover, only one function is needed to represent any numbers of phases. The itera...

In this work we consider the inverse problem of detecting inclusions or cavities in an elastic body, using a single boundary measurement on an external boundary. We discuss the identifiability questions on shape reconstruction, presenting counterexamples for Robin boundary conditions or with additional unknown Lamé parameters. Using the method of fundamental solutions (MFS) we adapt a method in...