Geodesic
Non-local problems with integral displacement for high-order parabolic equations
The Bulletin of Irkutsk State University. Series Mathematics, Tome 36 (2021), pp. 14-28

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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.
Keywords: high-order parabolic equations, non-local problems, integral boundary conditions, regular solutions, uniqueness
Mots-clés : existence. 
@article{IIGUM_2021_36_a1,
     author = {A. I. Kozhanov and A. V. Dyuzheva},
     title = {Non-local problems with integral displacement for high-order parabolic equations},
     journal = {The Bulletin of Irkutsk State University. Series Mathematics},
     pages = {14--28},
     publisher = {mathdoc},
     volume = {36},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IIGUM_2021_36_a1/}
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A. I. Kozhanov; A. V. Dyuzheva. Non-local problems with integral displacement for high-order parabolic equations. The Bulletin of Irkutsk State University. Series Mathematics, Tome 36 (2021), pp. 14-28. http://geodesic.mathdoc.fr/item/IIGUM_2021_36_a1/