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This article is cited in 2 scientific papers (total in 2 papers)
Differentical equations, dynamical systems and optimal control
On solvability of the boundary value problem for one pseudohyperbolic equation
L. N. Bondara, V. Nurmakhmatovb a Sobolev Institute of Mathematics, 4, Koptyuga ave., Novosibirsk, 630090, Russia
b Novosibirsk State University, 1, Pirogova str., Novosibirsk, 630090, Russia
Abstract:
The paper considers the first boundary value problem in a rectangle for the equation describing torsional vibrations of an elastic rod. Existence and uniqueness theorems are proved for a generalized solution of the first boundary value problem in Sobolev space.
Keywords:
generalized solution, pseudohyperbolic equation, torsional vibrations, Sobolev space, unique solvability, Galerkin method.
Received June 15, 2021, published October 19, 2021
Citation:
L. N. Bondar, V. Nurmakhmatov, “On solvability of the boundary value problem for one pseudohyperbolic equation”, Sib. Èlektron. Mat. Izv., 18:2 (2021), 1046–1057
Linking options:
https://www.mathnet.ru/eng/semr1421 https://www.mathnet.ru/eng/semr/v18/i2/p1046
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