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Zh. Vychisl. Mat. Mat. Fiz., 2010, Volume 50, Number 3, Pages 479–485 (Mi zvmmf4844)  

This article is cited in 7 scientific papers (total in 7 papers)

Asymptotic behavior of the solution of the Neumann problem with a delta-like boundary function

A. A. Ershov

Chelyabinsk State University, ul. Brat'ev Kashirinukh 129, Chelyabinsk, 454136 Russia

Abstract: A uniform asymptotic expansion is found for the integral $\iint_S\nabla^2 u  dx dy$, where $u$ is the solution of the Neumann problem with a delta-function-like derivative on the boundary. A physics application of the result is discussed.

Key words: Laplace equation, asymptotic expansion of an integral related to the Neumann problem, delta-function-like derivative.

Full text: PDF file (198 kB)
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English version:
Computational Mathematics and Mathematical Physics, 2010, 50:3, 457–463

Bibliographic databases:

UDC: 519.632.4
Received: 28.09.2009

Citation: A. A. Ershov, “Asymptotic behavior of the solution of the Neumann problem with a delta-like boundary function”, Zh. Vychisl. Mat. Mat. Fiz., 50:3 (2010), 479–485; Comput. Math. Math. Phys., 50:3 (2010), 457–463

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. A. A. Ershov, “Asymptotics of the solution of Laplace's equation with mixed boundary conditions”, Comput. Math. Math. Phys., 51:6 (2011), 994–1010  mathnet  crossref  mathscinet  isi  elib
    2. Dmitriev A.V., Ershov A.A., “Electrophysical properties of composition based on natural flake graphite and binder”, Solid Fuel Chemistry, 45:6 (2011), 411–417  crossref  mathscinet  zmath  isi  elib  elib  scopus
    3. A. A. Ershov, “On measurement of electrical conductivity”, Comput. Math. Math. Phys., 53:6 (2013), 823–826  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    4. R. R. Gadylshin, A. A. Ershov, S. V. Repyevsky, “On asymptotic formula for electric resistance of conductor with small contacts”, Ufa Math. J., 7:3 (2015), 15–27  mathnet  crossref  isi  elib
    5. A. A. Ershov, Yu. A. Krutova, “Asimptotika magnetosoprotivleniya”, Vestn. YuUrGU. Ser. Vych. matem. inform., 5:1 (2016), 5–12  mathnet  crossref  elib
    6. A. A. Ershov, “Contact resistance of a square contact”, Proc. Steklov Inst. Math. (Suppl.), 303, suppl. 1 (2018), 70–78  mathnet  crossref  crossref  isi  elib
    7. Yu. A. Krutova, “Kontaktnoe soprotivlenie pryamougolnogo kontakta”, Chelyab. fiz.-matem. zhurn., 6:2 (2021), 162–171  mathnet  crossref
  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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