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Vestnik Novosibirskogo Gosudarstvennogo Universiteta. Seriya Matematika, Mekhanika, Informatika, 2012, Volume 12, Issue 1, Pages 126–138 (Mi vngu113)  

This article is cited in 6 scientific papers (total in 6 papers)

Boundary value problems for third-order equations with discontinuous coefficient

V. V. Shubin

Novosibirsk State University, Novosibirsk, Russia
Full-text PDF (222 kB) Citations (6)
References:
Abstract: In the work we consider boundary value problems for third order equations with changing evolution direction $\operatorname{sign}yu_{yyyy}\pm Au+c(x,y)u= f(x,y)$ in the cylinder $Q=\Omega\times(-T,T)=\{(x,y)\colon x\in\Omega,\ -T<y<T\}$, where $\Omega$ is connected subser of $\mathbb R^n$ that have smooth boundary and $T>0$. Here $A$ is elliptic operator $Au=\frac\partial{\partial x_j}\big(a^{ij}(x)u_{x_i}\big)$. It is assigned boundary conditions on lateral surface $\partial\Omega\times(-T,T)$ of cylinder $Q$ and on bases $\Omega\times\{-T\}$ and $\Omega\times\{T\}$ of cylinder for these equations. Also we assign coupling conditions on section $\Omega\times0$. We prove theorems of existence and uniquness of regular solutions of these problems.
Keywords: partial differential equations, third-order equations, equations of composite type, equations with variable direction of evolution, equations with discontinuous coefficients.
Received: 04.03.2011
English version:
Journal of Mathematical Sciences, 2014, Volume 198, Issue 5, Pages 637–647
DOI: https://doi.org/10.1007/s10958-014-1815-1
Document Type: Article
UDC: 517.95
Language: Russian
Citation: V. V. Shubin, “Boundary value problems for third-order equations with discontinuous coefficient”, Vestn. Novosib. Gos. Univ., Ser. Mat. Mekh. Inform., 12:1 (2012), 126–138; J. Math. Sci., 198:5 (2014), 637–647
Citation in format AMSBIB
\Bibitem{Shu12}
\by V.~V.~Shubin
\paper Boundary value problems for third-order equations with discontinuous coefficient
\jour Vestn. Novosib. Gos. Univ., Ser. Mat. Mekh. Inform.
\yr 2012
\vol 12
\issue 1
\pages 126--138
\mathnet{http://mi.mathnet.ru/vngu113}
\transl
\jour J. Math. Sci.
\yr 2014
\vol 198
\issue 5
\pages 637--647
\crossref{https://doi.org/10.1007/s10958-014-1815-1}
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  • https://www.mathnet.ru/eng/vngu/v12/i1/p126
  • This publication is cited in the following 6 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Вестник Новосибирского государственного университета. Серия: математика, механика, информатика
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    Abstract page:250
    Full-text PDF :94
    References:45
    First page:11
     
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