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Zh. Vychisl. Mat. Mat. Fiz., 2011, Volume 51, Number 3, Pages 436–455 (Mi zvmmf8072)  

This article is cited in 1 scientific paper (total in 1 paper)

Study of classical solution of a one-dimensional mixed problem for one class of fifth-order semilinear equations of the Korteweg–de Vries–Burgers type

M. H. Sadykhov, K. I. Khudaverdiev

Faculty of Mechanics and Mathematics, Baku State University, ul. Z. Khalilova 23, Baku, AZ1148 Azerbaijan

Abstract: As is well known, many problems of mathematical physics are reduced to one- and multi-dimensional initial and initial–boundary value problems for, generally speaking, strongly nonlinear pseudoparabolic equations. The existence (local and global) and uniqueness of a classical solution to a one-dimensional mixed problem with homogeneous Riquier-type boundary conditions are analyzed for a class of fifth-order semilinear pseudoparabolic equations of the Korteweg–de Vries–Burgers type. For the classical solution of the mixed problem, a uniqueness theorem is proved using the Gronwall–Bellman inequality, a local existence theorem is proved by combining the generalized contraction mapping principle with the Schauder fixed point principle, and a global existence theorem is proved by applying the method of a priori estimates.

Key words: pseudoparabolic equation, mixed problem, classical solution, local existence of solutions, global existence of solutions, fixed point principles, a priori estimates.

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English version:
Computational Mathematics and Mathematical Physics, 2011, 51:3, 404–422

Bibliographic databases:

UDC: 519.633
Received: 09.10.2009

Citation: M. H. Sadykhov, K. I. Khudaverdiev, “Study of classical solution of a one-dimensional mixed problem for one class of fifth-order semilinear equations of the Korteweg–de Vries–Burgers type”, Zh. Vychisl. Mat. Mat. Fiz., 51:3 (2011), 436–455; Comput. Math. Math. Phys., 51:3 (2011), 404–422

Citation in format AMSBIB
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\by M.~H.~Sadykhov, K.~I.~Khudaverdiev
\paper Study of classical solution of a~one-dimensional mixed problem for one class of fifth-order semilinear equations of the Korteweg--de Vries--Burgers type
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 2011
\vol 51
\issue 3
\pages 436--455
\mathnet{http://mi.mathnet.ru/zvmmf8072}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2839574}
\transl
\jour Comput. Math. Math. Phys.
\yr 2011
\vol 51
\issue 3
\pages 404--422
\crossref{https://doi.org/10.1134/S0965542511030109}
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\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-79953687999}


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    This publication is cited in the following articles:
    1. Sh. Amirov, A. I. Kozhanov, “Razreshimost smeshannoi zadachi dlya nekotorykh silno nelineinykh uravnenii sobolevskogo tipa vysokogo poryadka”, Sib. zhurn. industr. matem., 17:4 (2014), 14–30  mathnet  mathscinet
  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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