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Vladikavkaz. Mat. Zh., 2013, Volume 15, Number 3, Pages 19–36 (Mi vmj468)  

This article is cited in 5 scientific papers (total in 5 papers)

A priori estimates of the solutions of nonlocal boundary value problems for a pseudo-parabolic equation

M. H. Beshtokov

Kabardino-Balkar State University, Nal'chik, Russia

Abstract: In this paper we consider nonlocal boundary value problems for a third order pseudo-parabolic equation with variable coefficients in the one-dimensional and multidimensional cases. For nonlocal problems a priori estimates in differential and difference treatment are obtained. These estimates imply uniqueness, stability and convergence of the solution of the difference problem to the solution of the differential problem.

Key words: boundary value problem, nonlocal condition, a priori estimate, difference scheme, stability and convergence of difference schemes, hyperbolic equation of the third order, pseudo-parabolic equation.

Full text: PDF file (199 kB)
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UDC: 519.635
Received: 14.05.2012

Citation: M. H. Beshtokov, “A priori estimates of the solutions of nonlocal boundary value problems for a pseudo-parabolic equation”, Vladikavkaz. Mat. Zh., 15:3 (2013), 19–36

Citation in format AMSBIB
\Bibitem{Bes13}
\by M.~H.~Beshtokov
\paper A priori estimates of the solutions of nonlocal boundary value problems for a~pseudo-parabolic equation
\jour Vladikavkaz. Mat. Zh.
\yr 2013
\vol 15
\issue 3
\pages 19--36
\mathnet{http://mi.mathnet.ru/vmj468}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Stikonas A., “A Survey on Stationary Problems, Green'S Functions and Spectrum of Sturm-Liouville Problem With Nonlocal Boundary Conditions”, Nonlinear Anal.-Model Control, 19:3, SI (2014), 301–334  crossref  mathscinet  zmath  isi  scopus
    2. T. K. Yuldashev, “Obratnaya zadacha dlya integro-differentsialnogo uravneniya Fredgolma tretego poryadka s vyrozhdennym yadrom”, Vladikavk. matem. zhurn., 18:2 (2016), 76–85  mathnet
    3. E. A. Sozontova, “K usloviyam razreshimosti zadachi Gursa v kvadraturakh dlya dvumernoi sistemy vysokogo poryadka”, Vestn. Sam. gos. tekhn. un-ta. Ser. Fiz.-mat. nauki, 21:1 (2017), 94–111  mathnet  crossref  elib
    4. O. M. Kechina, “O razreshimosti nelokalnoi zadachi dlya uravneniya tretego poryadka”, Vestn. SamU. Estestvennonauchn. ser., 2017, no. 1, 15–20  mathnet  elib
    5. M. H. Yagubov, Sh. Sh. Yusubov, “The Goursat problem for the pseudoparabolic equation of the third order with singular coefficients”, Proceedings of the 6Th International Conference on Control and Optimization With Industrial Applications, v. I, eds. A. Fikret, B. Tamer, Baku State Univ., Inst. Applied Mathematics, 2018, 376–378  isi
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