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.
Keywords:
hyperbolic equations, parabolic equations, integral boundary conditions, nonlocal problems, integral conditions, regular solutions, uniqueness, existence.
The work was carried out with the financial support of the Ministry of education and science of the Russian Federation in the framework of state task no. 0778–2020–0005.
Citation:
A. I. Kozhanov, A. V. Dyuzheva, “The second initial-boundary value problem with integral displacement for second-order hyperbolic and parabolic equations”, Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 25:3 (2021), 423–434
\Bibitem{KozDyu21}
\by A.~I.~Kozhanov, A.~V.~Dyuzheva
\paper The second initial-boundary value problem with integral displacement for second-order hyperbolic and parabolic equations
\jour Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.]
\yr 2021
\vol 25
\issue 3
\pages 423--434
\mathnet{http://mi.mathnet.ru/vsgtu1859}
\crossref{https://doi.org/10.14498/vsgtu1859}
\zmath{https://zbmath.org/?q=an:7499952}
\elib{https://elibrary.ru/item.asp?id=46801514}
\edn{https://elibrary.ru/ZAKEGT}
This publication is cited in the following 7 articles:
A. Yu. Trynin, “Ob odnom metode resheniya smeshannoi kraevoi zadachi dlya uravneniya parabolicheskogo tipa s pomoschyu operatorov ATλ,j”, Izv. vuzov. Matem., 2024, no. 2, 59–80
A. Yu. Trynin, “On One Method for Solving a Mixed Boundary Value Problem for a Parabolic Type Equation Using Operators ATλ,j”, Russ Math., 68:2 (2024), 52
A. Yu. Trynin, “A method for solution of a mixed boundary value problem for a hyperbolic type equation using the operators ATλ,j”, Izv. Math., 87:6 (2023), 1227–1254
A. Yu. Trynin, “On a method for solving a mixed boundary value problem for a parabolic equation using modified sinc-approximation operators”, Comput. Math. Math. Phys., 63:7 (2023), 1264–1284
A. I. Kozhanov, A. V. Dyuzheva, “Integral Analogue of the First Initial-Boundary Value Problem for Second-Order Hyperbolic and Parabolic Equations”, Math. Notes, 111:4 (2022), 562–570
A. B. Beilin, A. V. Bogatov, L. S. Pulkina, “Zadacha s nelokalnymi usloviyami dlya odnomernogo parabolicheskogo uravneniya”, Vestn. Sam. gos. tekhn. un-ta. Ser. Fiz.-mat. nauki, 26:2 (2022), 380–395
A. V. Bogatov, A. V. Gilev, L. S. Pulkina, “Zadacha s nelokalnym usloviem dlya uravneniya chetvertogo poryadka s kratnymi kharakteristikami”, Vestnik rossiiskikh universitetov. Matematika, 27:139 (2022), 214–230
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