STABILITY OF THE DIFFERENTIAL-DIFFERENCE ANALOG OF THE INTEGRAL GEOMETRY PROBLEM WITH A WEIGHT FUNCTION

Abstract

In this paper, we consider the problem of Integral geometry, which is brought to the problem of difference for a mixed-type equation for a bunch of curves that satisfy some regularity conditions. The study of distinctive analogues of Integral geometry problems has its own complex points, due to the fact that for limited-distinctive analogues of independent derivatives, the main relations are carried out with a certain shift over a discrete variable. Therefore, many relationships obtained in continuous representation take on a more complex form when switching to a discrete analog, and require further research on the connectors that occur duringthe shift. Since these problems do not have a theorem on the existence of a solution in the general case, the concept of conditional correctness is used, that is, it is assumed that the problem of Integral geometry and its differential-differential analoghave a solution. The stability assessment of the differential analog of the boundary problem for the mixed-type equation obtained in the work is carried out by geotomography, medical tomography, defectoscopy, etc. it is used to justify the compactness of numerical problem solving methods.