Volume 15, Issue 6

The work is devoted to constructive methods of investigating multi-dimensional inverse problems for evolution equations. We present formulas and relations for solutions and coefficients of evolution equations and inverse problems.

The article is devoted to a Lagrange principle application to a problem of optimal recovery of a linear functional value on a solution of a linear integral equation. Problems of solving Fredholm integral equations of the first and second kind and the Abel integral equation are considered. A priori information on a solution is included in a statement of problems. The algorithms of optimal recovery of linear functionals on solutions are described.

We prove the unique continuation property for the hyperbolic integro-differential equation

We prove existence and uniqueness for an unknown coefficient, depending on space only, entering in an initial boundary value problem arising in absorption dynamics, where diffusion is also taken into account.

This paper deals with a two or three dimensional inverse scattering problem for identifying a sound hard obstacle in a homogeneous medium. We provide a reconstruction scheme for identifying the obstacle from far field patterns of scattered waves associated with incident waves in all directions when the obstacle is not necessarily convex.

The short review of methods of reconstruction non-smooth solutions to ill-posed problems is presented. In the Tikhonov method for some parametric classes of stabilizing functionals the convergence theorems for regularized solutions and their discrete approximations are stated. The questions concerning the numerical algorithms are considered.