The inverse problem of amplitude reconstruction on an inclined line based the values or its module as recorded semi-infinite orthogonal to beam propagation direction is considered within framework 2D parabolic equation. It demonstrated that this problem, in case when complex image plane known, can be reduced a singular Cauchy type integral existence solutions requires certain conditions met but...

Abstract: In this paper a type of inverse problem belongs to the class of parabolic equations is considered. The approximation of the problem is based on the Ritz-Galerkin method. This approximation provides greater flexibility in which to impose initial and boundary conditions. The results of numerical experiments are compared with analytical solutions and perspicuous examples are included to ...

A review of the author’s results is given. Inversion formulas and stability results for the solutions to 3D inverse scattering problems with fixed energy data are obtained. Inversion of exact and noisy data is considered. The inverse potential scattering problem with fixed-energy scattering data is discussed in detail, inversion formulas for the exact and for noisy data are derived, error estim...

in this paper, at rst for a given set of real or complex numbers  with nonnegative summation, we introduce some special conditions that with them there is no nonnegative tridiagonal matrix in which  is its spectrum. in continue we present some conditions for existence such nonnegative tridiagonal matrices.

In the present article we study inverse problem of determining a general semilinear term for class nonlinear parabolic equations. We derive new criterion unique and stable recovery terms these type equations from knowledge Dirichlet-to-Neumann map associated with solutions equation having zero initial data.

This article is devoted to the study of an inverse source problem for a mixed type equation with fractional diffusion in parabolic part and wave hyperbolic cylindrical domain. The solution obtained form FourierBessel series expansion using orthogonal set Bessel functions. theorems uniqueness existence are proved.