This paper deals with an inverse problem for identifying an unknown source which depends only on one variable in two-dimensional Poisson equation, with the aid of an extra measurement at an internal point. Since this problem is illposed, we obtain the regularization solution by the modified regularization method. Furthermore, we obtain the Hölder-type error estimate between the regularization s...

In this paper, we will use a modified  variational iteration method (MVIM) for solving an inverse heat conduction problem (IHCP). The approximation of the temperature and the heat flux at  are considered. This method is based on the use of Lagrange multipliers for the identification of optimal values of parameters in a functional in Euclidian space. Applying this technique, a rapid convergent s...

In the present paper, we solve the problem of reducing to the simplest and convenient for our purposes, “canonical” form for an arbitrary pair of compatible nonlocal Poisson brackets of hydrodynamic type generated by metrics of constant Riemannian curvature (compatible Mokhov–Ferapontov brackets [1]) in order to get an effective construction of the integrable hierarchies related to all these co...

The inverse problem associated with reconstruction of Poisson blurred images arising from many fields ranging from engineering to medicine has attracted much attention in the recent years. Digital images captured at medium to low light levels are often corrupted by sensor noise which is dominated by Poisson statistics. The zoom optics, sensor PSF and atmospheric turbulence cause blurring in acq...

A rigorous theory of the inverse scattering transform for the defocusing nonlinear Schrödinger equation with nonvanishing boundary values q± ≡ q0e± as x → ±∞ is presented. The direct problem is shown to be well posed for potentials q such that q − q± ∈ L1,2(R±), for which analyticity properties of eigenfunctions and scattering data are established. The inverse scattering problem is formulated a...

The recovery of the coe cient H(x) in the one-dimensional generalized Schrodinger equation d =dx + kH(x) = Q(x) ; where H(x) is a positive, piecewise continuous function with positive limits H as x ! 1; is studied. The large-k asymptotics of the wavefunctions and the scattering coe cients are analyzed. A factorization formula is given expressing the total scattering matrix as a product of simp...

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 study the inverse electrostatic and elasticity problems associated with Poisson and Navier equations. These problems arise in a number of applications, such as diagnostic of electronic devices and analysis of residual stresses in materials. In microelectronics, piecewise constant distributions of electric charge having a checkered structure (i.e., that are constant on rectangular blocks) are...