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Sib. J. Pure and Appl. Math., 2016, Volume 16, Issue 3, Pages 103–117 (Mi vngu415)  

Some equations with partial derivative of high order

N. A. Chuesheva

Kemerovo State University

Abstract: In this article are a boundary problems for linear and non linear equation with partial derivative of order higher than two considered. For some conditions on coefficients of equation are proven an uniqueness and existence theorems. If conditions on coefficients differential equation are not fulfilled or changed of boundary conditions then given a examples solutions these problems, which will be non uniquely, non stable and will not belong to Sobolev space. Moreover, also given a exactly solutions for equations of Korteweg–de Vries, Kadomzeva–Petviashwili.

Keywords: uniqueness solution, existence solution, spaces of S. L. Sobolev, stability solution, boundary problem, equation of Korteweg–de Vries.

DOI: https://doi.org/10.17377/PAM.2016.16.310

Full text: PDF file (208 kB)
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UDC: 517.95
Received: 22.12.2015

Citation: N. A. Chuesheva, “Some equations with partial derivative of high order”, Sib. J. Pure and Appl. Math., 16:3 (2016), 103–117

Citation in format AMSBIB
\Bibitem{Chu16}
\by N.~A.~Chuesheva
\paper Some equations with partial derivative of high order
\jour Sib. J. Pure and Appl. Math.
\yr 2016
\vol 16
\issue 3
\pages 103--117
\mathnet{http://mi.mathnet.ru/vngu415}
\crossref{https://doi.org/10.17377/PAM.2016.16.310}


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