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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2012, Volume 52, Number 10, Pages 1855–1865 (Mi zvmmf9767)  
This article is cited in 1 scientific paper (total in 1 paper)

On the initial boundary value problem for a nonlinear nonhomogeneous equation of Sobolev type

A. I. Aristov

Faculty of Computational Mathematics and Cybernetics, Moscow State University, Moscow, Russia
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Abstract: The initial boundary value problem for a nonlinear nonhomogeneous equation of Sobolev type used for modeling nonstationary processes in semiconductors is examined. It is proved that this problem is uniquely solvable at least locally in time. Sufficient conditions for the problem to be solvable globally in time are found, as well as sufficient conditions for the local (but not global) solvability. In the case of only local solvability, upper and lower estimates for the time when a solution exists are determined in the form of either explicit or quadrature formulas.
Key words: initial boundary value problem for an equation of Sobolev type, conditions for the destruction of solutions, method of energy estimates.
Received: 16.06.2011
Revised: 27.02.2012
English version:
Computational Mathematics and Mathematical Physics, 2012, Volume 52, Issue 10, Pages 1417–1427
DOI: https://doi.org/10.1134/S0965542512100041
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: A. I. Aristov, “On the initial boundary value problem for a nonlinear nonhomogeneous equation of Sobolev type”, Zh. Vychisl. Mat. Mat. Fiz., 52:10 (2012), 1855–1865; Comput. Math. Math. Phys., 52:10 (2012), 1417–1427
Citation in format AMSBIB
\Bibitem{Ari12}
\by A.~I.~Aristov
\paper On the initial boundary value problem for a nonlinear nonhomogeneous equation of Sobolev type
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 2012
\vol 52
\issue 10
\pages 1855--1865
\mathnet{http://mi.mathnet.ru/zvmmf9767}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3150296}
\zmath{https://zbmath.org/?q=an:1274.35022}
\transl
\jour Comput. Math. Math. Phys.
\yr 2012
\vol 52
\issue 10
\pages 1417--1427
\crossref{https://doi.org/10.1134/S0965542512100041}
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    • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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