Abstract: The aim of this paper is to study the solvability of solutions of non-local problems with integral conditions in spatial variables for high-order linear parabolic equations in the classes of regular solutions (which have all the squared derivatives generalized by S. L. Sobolev that are included in the corresponding equation) . Previously, similar problems were studied for high-order parabolic equations, either in the one-dimensional case, or when certain conditions of smallness on the coefficients are met equations. In this paper, we present new results on the solvability of non-local problems with integral spatial variables for high-order parabolic equations a) in the multidimensional case with respect to spatial variables; b) in the absence of smallness conditions. The research method is based on the transition from a problem with non-local integral conditions to a problem with classical homogeneous conditions of the first or second kind on the side boundary for a loaded integro-differential equation. At the end of the paper, some generalizations of the obtained results will be described. © 2021 Irkutsk State University. All rights reserved.

Cite: Kozhanov A.I. , Dyuzheva A.V.
Non-local problems with integral displacement for highorder parabolic equations
Известия Иркутского государственного университета. Серия: Математика (Bulletin of Irkutsk State University. Series Mathematics). 2021. V.36. P.14-28. DOI: 10.26516/1997-7670.2021.36.14 WOS Scopus OpenAlex

Identifiers:

Web of science:	WOS:000662709100002
Scopus:	2-s2.0-85109330229
OpenAlex:	W3176520404

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Scopus	4
OpenAlex	6
Web of science	1

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