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Mat. Sb., 1996, Volume 187, Number 10, Pages 3–32 (Mi msb162)  

This article is cited in 9 scientific papers (total in 9 papers)

Asymptotic solution of the Signorini problem with an obstacle on a thin elongated set

I. I. Argatova, S. A. Nazarovb

a Saint-Petersburg State University
b Admiral Makarov State Maritime Academy

Abstract: The Signorini problem for a Poisson equation is studied subject to onesided constraints imposed on a narrow annular boundary band $\Gamma _\varepsilon$ (of width $O(\varepsilon )$). An asymptotic analysis yields a resultant variational inequality on the contour $\Gamma$ to which $\Gamma _\varepsilon$ contracts as $\varepsilon \to 0$. Approximate solutions of the resultant inequality are derived with varying degree of accuracy and used to construct and justify an asymptotic solution of the original Signorini problem.

DOI: https://doi.org/10.4213/sm162

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English version:
Sbornik: Mathematics, 1996, 187:10, 1411–1442

Bibliographic databases:

UDC: 517.953
MSC: Primary 35C20; Secondary 35B20, 35J85
Received: 10.02.1995

Citation: I. I. Argatov, S. A. Nazarov, “Asymptotic solution of the Signorini problem with an obstacle on a thin elongated set”, Mat. Sb., 187:10 (1996), 3–32; Sb. Math., 187:10 (1996), 1411–1442

Citation in format AMSBIB
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\jour Mat. Sb.
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\issue 10
\pages 3--32
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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. Argatov, II, “Asymptotic solution of the problem of the pressure of a rigid body on a membrane”, Pmm Journal of Applied Mathematics and Mechanics, 64:4 (2000), 659  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    2. Argatov, II, “Propagation of a mode-I crack under the irwin and Khristianovich-Barenblatt criteria”, Materials Science, 39:3 (2003), 365  crossref  isi  elib  scopus  scopus
    3. I. I. Argatov, J. Sokolowski, “Asymptotics of the energy functional in the Signorini problem under small singular perturbation of the domain”, Comput. Math. Math. Phys., 43:5 (2003), 710–724  mathnet  mathscinet  zmath  elib
    4. M. Yu. Planida, “Asymptotics of the Eigenelements of the Laplace Operator when the Boundary-Condition Type Changes on a Narrow Flattened Strip”, Math. Notes, 75:2 (2004), 213–228  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    5. M. Yu. Planida, “Asymptotics of the eigenelements of the Laplacian with singular perturbations of boundary conditions on narrow and thin sets”, Sb. Math., 196:5 (2005), 703–741  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    6. O. V. Izotova, S. A. Nazarov, “An asymptotic solution to the Signorini problem about a beam laying on two rigid bases”, J. Math. Sci. (N. Y.), 138:2 (2006), 5503–5513  mathnet  crossref  mathscinet  zmath  elib
    7. Sokolowski, J, “Modelling of topological derivatives for contact problems”, Numerische Mathematik, 102:1 (2005), 145  crossref  mathscinet  zmath  isi  elib  scopus  scopus
    8. Sokolowski J., Zochowski A., “Topology optimization for unilateral problems”, Calorimetry in Particle Physics, Lecture Notes in Pure and Applied Mathematics, 240, 2005, 97–105  crossref  mathscinet  zmath  isi
    9. Argatov I.I., Mishuris G.S., “Contact Problem For Thin Biphasic Cartilage Layers: Perturbation Solution”, Quart J Mech Appl Math, 64:3 (2011), 297–318  crossref  mathscinet  zmath  isi  elib  scopus  scopus
  • Математический сборник - 1992–2005 Sbornik: Mathematics (from 1967)
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