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Zhurnal Srednevolzhskogo Matematicheskogo Obshchestva, 2019, Volume 21, Number 4, Pages 413–429
DOI: https://doi.org/10.15507/2079-6900.21.201904.413-429
(Mi svmo750)
 

This article is cited in 3 scientific papers (total in 3 papers)

Mathematics

On the connection between solutions of initial boundary-value problems for a some class of integro-differential PDE and a linear hyperbolic equation

P. N. Burago, A. I. Egamov

National Research Lobachevsky State University of Nizhny Novgorod
Full-text PDF (274 kB) Citations (3)
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Abstract: We consider the second initial boundary-value problem for a certain class of second-order integro-differential PDE with integral operator. The connection of its solution with the solution of the standard second linear initial boundary-value problem for the hyperbolic equation is shown. Thus, the nonlinear problem is reduced to a standard linear problem, whose numerical solution can be obtained, for example, by the Fourier method or Galerkin method. The article provides examples of five integro-differential equations for various integral operators as particular representatives of the class of integro-differential equations for a better understanding of the problem. The application of the main theorem to these examples is shown. Some simple natural requirement is imposed on the integral operator; so, in four cases out of five the problem's solution satisfies some phase constraint. The form of these constraints is of particular interest for the further research.
Keywords: the second initial boundary value problem, integro-differential equation with PDE, phase constraint, hyperbolic equation.
Document Type: Article
UDC: 517.956.3
MSC: 35L20
Language: Russian
Citation: P. N. Burago, A. I. Egamov, “On the connection between solutions of initial boundary-value problems for a some class of integro-differential PDE and a linear hyperbolic equation”, Zhurnal SVMO, 21:4 (2019), 413–429
Citation in format AMSBIB
\Bibitem{BurEga19}
\by P.~N.~Burago, A.~I.~Egamov
\paper On the connection between solutions of initial boundary-value problems for a some class of integro-differential PDE and a linear hyperbolic equation
\jour Zhurnal SVMO
\yr 2019
\vol 21
\issue 4
\pages 413--429
\mathnet{http://mi.mathnet.ru/svmo750}
\crossref{https://doi.org/10.15507/2079-6900.21.201904.413-429}
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  • This publication is cited in the following 3 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    Zhurnal Srednevolzhskogo Matematicheskogo Obshchestva
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