The second initial-boundary value problem with integral displacement for second-order hyperbolic and parabolic equations

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Abstract

In this paper, we study the solvability of some non-local analogs of the second initial-boundary value problem for multidimensional hyperbolic and parabolic equations of the second order. We prove the existence and uniqueness theorems of regular solutions (which have all Sobolev generalized derivatives that are summable with a square and are included in the equation). Some generalization and amplification of the obtained results are also given.

About the authors

Alexander I. Kozhanov

Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences; Samara State Technical University

Email: kozhanov@math.nsc.ru
ORCID iD: 0000-0003-4376-4003
SPIN-code: 9132-3234
Scopus Author ID: 55892833300
ResearcherId: R-5686-2016
http://www.mathnet.ru/person18220

Dr. Phys. & Math. Sci., Professor; Chief Researcher; Lab. of Differential and Difference Equations1; Professor; Dept. of Higher Mathematics2

4, Acad. Koptyug pr., Novosibirsk, 630090, Russian Federation; 244, Molodogvardeyskaya st., Samara, 443100, Russian Federation

Alexandra V. Dyuzheva

Samara State Technical University

Author for correspondence.
Email: duzhevaalexandra@yandex.ru
ORCID iD: 0000-0002-3284-5302
Scopus Author ID: 57221800436
http://www.mathnet.ru/person53016

Cand. Phys. & Math. Sci.; Associate Professor; Dept. of Higher Mathematics

244, Molodogvardeyskaya st., Samara, 443100, Russian Federation

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