Volume 13, Issue 5

The sufficient conditions of well-posedness of formulas for determining of two coefficients of an evolution equation are considered.

We consider the inverse boundary value problem concerning the determination and reconstruction of an unknown potential in a Schrödinger equation in a bounded domain from measurements on the boundary the domain. For the special case of a small potential homogeneous of degree zero we show that one boundary measurement determines the potential uniquely. Moreover, we give a reconstruction procedure.

In this paper, we discuss the structure of the solution space of system of operator equations of the first kind A i u = ƒ i , i = 1, 2, . . . , n in Hilbert spaces. If it has solutions, we give the analytic representation of all its solutions. Final examples show our methods are effective.

Browne and Sleemens's paper is concerning the determination of potential uniquely from the nodes for regular sturm liouville problem. In this paper, we show that the potential function in the Sturm—Liouville problem having singularity at the point zero can be determined from the position of the nodes for the eigenfunctions.

In this paper we determine, under a suitable additional information and in a framework of Gevrey-type functions with respect to the variable x 1 , the spatial part p ( x 1 , x 3 ) of the factorised kernel σ 1 ( x 1 , x 3 , t ) = p ( x 1 , x 3 ) k ( t ) in the integrodifferential Maxwell system related to a spatial domain of the form Ω × × + , where Ω is an interval in . In our context determining p means to show locally in space existence, uniqueness and continuous dependence of p on the data.

In this paper we shall give practical real inversion formulas of heat conduction on multidimensional spaces and show their numerical experiments by using computers.

The many-dimensional integral equation of the first kind is considered. The uniqueness theorem is proved in the class of analytic functions possessing values in a finite real algebra with division.

An inverse problem of spectral analysis is studied for non-selfadjoint singular systems of ordinary differential equations on the half-line in the case of multiplied roots of the characteristic polynomial. We give a formulation of the inverse problem, study properties of spectral characteristics, and prove the uniqueness theorem for the solution of the inverse problem.