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Kazan. Gos. Univ. Uchen. Zap. Ser. Fiz.-Mat. Nauki, 2006, Volume 148, Book 4, Pages 76–82 (Mi uzku575)  

This article is cited in 1 scientific paper (total in 1 paper)

On problems with displacement in boundary conditions for two partial differential equations

E. A. Utkina

Zelenodolsk Branch of Kazan State University

Abstract: In the present paper the system
$$ \sum_{i=0}^2\sum_{j=0}^ka_{ij}(x,y)D_x^iD_y^ju(x,y)=0,\quad k=1,2, $$
is investigated. The first equation of this system is the generalization of Aller's equation, and the second one is the generalization of Boussinesq–Love's equation. We consider the problems of finding the regular solutions of this system in the rectangle $D=\{x,y\in(0,1)\}$ by using the given linear relationships. The each of these relationships connect a values of unknown function in the boundary and the interior points of $D$ We obtain the sufficient conditions of existence of unique solutions of the considered problems in the terms of the coefficients of the above mentioned relationships.

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Bibliographic databases:
UDC: 517.956
Received: 18.12.2006

Citation: E. A. Utkina, “On problems with displacement in boundary conditions for two partial differential equations”, Kazan. Gos. Univ. Uchen. Zap. Ser. Fiz.-Mat. Nauki, 148, no. 4, Kazan University, Kazan, 2006, 76–82

Citation in format AMSBIB
\Bibitem{Utk06}
\by E.~A.~Utkina
\paper On problems with displacement in boundary conditions for two partial differential equations
\serial Kazan. Gos. Univ. Uchen. Zap. Ser. Fiz.-Mat. Nauki
\yr 2006
\vol 148
\issue 4
\pages 76--82
\publ Kazan University
\publaddr Kazan
\mathnet{http://mi.mathnet.ru/uzku575}
\zmath{https://zbmath.org/?q=an:1158.35336}


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    This publication is cited in the following articles:
    1. E. A. Sozontova, “K usloviyam razreshimosti zadachi Gursa v kvadraturakh dlya dvumernoi sistemy vysokogo poryadka”, Vestn. Sam. gos. tekhn. un-ta. Ser. Fiz.-mat. nauki, 21:1 (2017), 94–111  mathnet  crossref  elib
  • Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki
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