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Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.]:
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Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, 2017, Volume 21, Number 4, Pages 597–610
DOI: https://doi.org/10.14498/vsgtu1536
(Mi vsgtu1536)
 

This article is cited in 4 scientific papers (total in 4 papers)

Differential Equations and Mathematical Physics

The nonlocal boundary value problem with constant coefficients for the multidimensional mixed type equation of the first kind

S. Z. Djamalov

V. I. Romanovskiy Institute of Mathematics, Uzbekistan Academy of Sciences, Tashkent, 100041, Uzbekistan
Full-text PDF (678 kB) Citations (4)
(published under the terms of the Creative Commons Attribution 4.0 International License)
References:
Abstract: In this paper the unique solvability and smoothness of generalized solution of a nonlocal boundary value problem with constant coefficients for the multidimensional mixed type equation of the first kind in Sobolev spaces $W_{2}^{l }(Q)$, ($2\le l $ is integer number), have been proved. First, the unique solvability of the generalized solution from space $W_{2}^{2 }(Q)$ has been studied. Further, the uniqueness of the generalized solution of nonlocal boundary value problem with constant coefficients for the multidimensional mixed type equation was proved by a priory estimates. For the proof of the existence of the generalized solution, we used method of "$\varepsilon$-regularization" together with Galerkin method. Precisely, first, we study regular solvability of the nonlocal boundary value problem for the multidimensional mixed type equation by functional analysis methods, i.e. we obtained necessary a priory estimates for the considered problems. Using these estimates we solve composite type equation, then by the theorem on weak compactness, we pass to the limit and deduce to the multidimensional mixed type equation of the first kind. At the end, smoothness of the generalized solution of the considered problems has been discussed.
Keywords: multidimensional mixed type equations, nonlocal boundary value problem with constants coefficients, unique solvability, smoothness of the generalized solution, $\varepsilon$-regularization method, Galerkin method.
Received: March 22, 2017
Revised: November 28, 2017
Accepted: December 18, 2017
First online: December 22, 2017
Bibliographic databases:
Document Type: Article
UDC: 517.956.6
MSC: 35M10, 35M12
Language: Russian
Citation: S. Z. Djamalov, “The nonlocal boundary value problem with constant coefficients for the multidimensional mixed type equation of the first kind”, Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 21:4 (2017), 597–610
Citation in format AMSBIB
\Bibitem{Dja17}
\by S.~Z.~Djamalov
\paper The nonlocal boundary value problem with constant coefficients for the multidimensional mixed type equation of the first kind
\jour Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.]
\yr 2017
\vol 21
\issue 4
\pages 597--610
\mathnet{http://mi.mathnet.ru/vsgtu1536}
\crossref{https://doi.org/10.14498/vsgtu1536}
\zmath{https://zbmath.org/?q=an:06964877}
\elib{https://elibrary.ru/item.asp?id=32712827}
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  • https://www.mathnet.ru/eng/vsgtu/v221/i4/p597
  • This publication is cited in the following 4 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Вестник Самарского государственного технического университета. Серия: Физико-математические науки
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    Full-text PDF :248
    References:63
     
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