Vestnik of Samara University. Natural Science SeriesVestnik of Samara University. Natural Science Series2541-75252712-8954Samara National Research University833110.18287/2541-7525-2020-26-2-15-22Research ArticleON SMOOTHNESS OF SOLUTION OF ONE NONLOCAL PROBLEM FOR HYPERBOLIC EQUATIONKirichekV. A.<p>postgraduate student, Department of Differential Equations and Control Theory</p>Vitalya29@gmail.comhttps://orcid.org/0000-0001-9817-863XSamara National Research University2706202026215220102202101022021Copyright © 2020, Kirichek V.A.2020<p>In this paper we consider a nonlocal problem with integral boundary condition for hyperbolic equation. The conditions of the problem contain derivatives of the first order with respect to both x and t,, which can be interpreted as an elastic fixation of the right end rod in the presence of a certain damper, and since the conditions also contain integral of the desired solution, this condition is nonlocal. It is known that problems with nonlocal integral conditions are non-self-adjoint and, therefore, the study of solvability encounters difficulties that are not characteristic of self-adjoint problems. Additional difficulties arise also due to the fact that one of the conditions is dynamic. The attention of the article is focused on studying the<br>smoothness of the solution of the nonlocal problem. The concept of a generalized solution is introduced, and the existence of second-order derivatives and their belonging to the space L2 are proved. The proof is based<br>on apriori estimates obtained in this work.</p>нелокальные условия, динамические граничные условия, гиперболическое
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