Mathematical modeling

Solvability of Gevrey boundary value problems for high order differential equation

S. V. Popov^a, Popova Michiye N<sup>b

a</sup> Academy of Science of the Republic of Sakha (Yakutia)
^b North-Eastern Federal University named after M. K. Ammosov, Yakutsk

Abstract: Singular integral operators of Gevrey problems for high-order parabolic equations with weighted conjugation (gluing) conditions are considered. In contrast to the classical case, the singular Cauchy operator together with the noncompact integral operators of a special form whose kernels are approximately homogeneous of degree−1 are among these operators. The Fredholm property criterion is established for these operators as well as formulas for their indexes. Examples of singular integral equations a rising in the study of boundary value problems for forward-backward equations are displayed.

Keywords: singular integral operators, integral operator with a kernel homogeneous of degree−1, Fredholm property criterion, formula for the index

UDC: 517.956.4

DOI: 10.25587/2411-9326-2025-2-100-101