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Sibirsk. Mat. Zh., 2003, Volume 44, Number 6, Pages 1350–1364 (Mi smj1261)  

This article is cited in 10 scientific papers (total in 10 papers)

The method of fictitious domains in the Signorini problem

V. D. Stepanova, A. M. Khludnevb

a Computer Centre Far-Eastern Branch of RAS
b M. A. Lavrent'ev Institute of Hydrodynamics

Abstract: We justify the method of fictitious domains for an elliptic equation with nonlinear Signorini boundary conditions. The method makes it possible to construct a family of auxiliary problems defined in a wider domain and possessing the property that their solutions converge in an appropriate sense to a solution of the original problem.

Keywords: Signorini boundary conditions, fictitious domain, elliptic boundary value problem

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English version:
Siberian Mathematical Journal, 2003, 44:6, 1061–1074

Bibliographic databases:

UDC: 517.95
Received: 24.04.2003

Citation: V. D. Stepanov, A. M. Khludnev, “The method of fictitious domains in the Signorini problem”, Sibirsk. Mat. Zh., 44:6 (2003), 1350–1364; Siberian Math. J., 44:6 (2003), 1061–1074

Citation in format AMSBIB
\by V.~D.~Stepanov, A.~M.~Khludnev
\paper The method of fictitious domains in the Signorini problem
\jour Sibirsk. Mat. Zh.
\yr 2003
\vol 44
\issue 6
\pages 1350--1364
\jour Siberian Math. J.
\yr 2003
\vol 44
\issue 6
\pages 1061--1074

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    This publication is cited in the following articles:
    1. Khludnev AM, “Invariant integrals in problems of a crack at the locus of inhomogeneity and in contact problems”, Doklady Physics, 49:10 (2004), 603–607  crossref  mathscinet  adsnasa  isi  scopus
    2. Fremiot G., Horn W., Laurain A., Rao M., Sokolowski J., “On the analysis of boundary value problems in nonsmooth domains”, Dissertationes Mathematicae, 2009, no. 462, 7  mathscinet  isi
    3. Alekseev G.V., Khludnev A.M., “Treschina v uprugom tele, vykhodyaschaya na granitsu pod nulevym uglom”, Vestn. Novosibirskogo gos. un-ta. Ser.: Matem., mekh., inform., 9:2 (2009), 15–29  zmath
    4. G. V. Alekseev, A. M. Khludnev, “Treschina v uprugom tele, vykhodyaschaya na granitsu pod nulevym uglom”, Vestn. NGU. Ser. matem., mekh., inform., 9:2 (2009), 15–29  mathnet
    5. N. P. Lazarev, “Fictitious domain method in the equilibrium problem for a Timoshenko-type plate contacting with a rigid obstacle”, J. Math. Sci., 203:4 (2014), 527–539  mathnet  crossref
    6. N. A. Nikolaeva, “Method of fictitious areas in a task about balance of a plate of Kirchhoff–Lyava”, J. Math. Sci., 221:6 (2017), 872–882  mathnet  crossref  crossref
    7. Lazarev N.P., Itou H., Neustroeva N.V., “Fictitious Domain Method For An Equilibrium Problem of the Timoshenko-Type Plate With a Crack Crossing the External Boundary At Zero Angle”, Jpn. J. Ind. Appl. Math., 33:1 (2016), 63–80  crossref  mathscinet  zmath  isi  scopus
    8. Lazarev N., Popova T., Semenova G., “Existence of An Optimal Size of a Rigid Inclusion For An Equilibrium Problem of a Timoshenko Plate With Signorini-Type Boundary Condition”, J. Inequal. Appl., 2016, 18  crossref  mathscinet  isi  scopus
    9. Nyurgun P. Lazarev, Vladimir V. Everstov, Natalya A. Romanova, “Fictitious domain method for equilibrium problems of the Kirchhoff–Love plates with nonpenetration conditions for known configurations of plate edges”, Zhurn. SFU. Ser. Matem. i fiz., 12:6 (2019), 674–686  mathnet  crossref
    10. I. V. Fankina, “O ravnovesii dvusloinoi uprugoi konstruktsii pri nalichii treschiny”, Sib. zhurn. industr. matem., 22:4 (2019), 107–120  mathnet  crossref
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