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Zh. Vychisl. Mat. Mat. Fiz., 2014, Volume 54, Number 8, Pages 1249–1255 (Mi zvmmf10072)  

This article is cited in 2 scientific papers (total in 2 papers)

On the asymptotics of the solution of the Dirichlet problem for a fourth-order equation in a layer

V. A. Nikishkin

Moscow State University of Economics, Statistics, and Informatics, ul. Nezhinskaya 7, Moscow, 119501, Russia

Abstract: The Dirichlet problem for a fourth-order elliptic equation with constant coefficients without first derivatives is considered in the region (layer)
$$ \Pi = \{ (x',x_n ) \in R^n | x' \in R^{n - 1}, x_n \in (a,b) \},\quad - \infty < a < b < + \infty, \quad n \geqslant 3. $$
The first term of the asymptotics of the solution at infinity is obtained.

Key words: asymptotics of solution, elliptic equation in a layer, fundamental solution, Dirichlet problem, estimates of solutions, Meijer $G$-function.

DOI: https://doi.org/10.7868/S0044466914080122

Full text: PDF file (201 kB)
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English version:
Computational Mathematics and Mathematical Physics, 2014, 54:8, 1214–1220

Bibliographic databases:

UDC: 519.635.4
MSC: 35J30,31B30
Received: 05.11.2013
Revised: 21.01.2014

Citation: V. A. Nikishkin, “On the asymptotics of the solution of the Dirichlet problem for a fourth-order equation in a layer”, Zh. Vychisl. Mat. Mat. Fiz., 54:8 (2014), 1249–1255; Comput. Math. Math. Phys., 54:8 (2014), 1214–1220

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. T. K. Yuldashev, “Obratnaya zadacha dlya nelineinogo integro-differentsialnogo uravneniya Fredgolma chetvertogo poryadka s vyrozhdennym yadrom”, Vestn. Sam. gos. tekhn. un-ta. Ser. Fiz.-mat. nauki, 19:4 (2015), 736–749  mathnet  crossref  zmath  elib
    2. D. A. Tursunov, G. A. Omaralieva, “Asimptotika resheniya dvukhzonnoi dvukhtochechnoi kraevoi zadachi”, Vestn. Yuzhno-Ur. un-ta. Ser. Matem. Mekh. Fiz., 13:2 (2021), 46–52  mathnet  crossref
  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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