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Mat. Sb., 2002, Volume 193, Number 3, Pages 101–114 (Mi msb638)  

This article is cited in 5 scientific papers (total in 5 papers)

On the homogenization of semilinear elliptic operators in perforated domains

H. Matevossian, S. V. Pikulin

M. V. Lomonosov Moscow State University

Abstract: A second-order semilinear elliptic equation whose lower term has power-like growth at infinity with respect to the unknown function is considered. It is proved that a sequence of its solutions in perforated domains converges to a solution in the non-perforated domain as the diameters of the holes converge to zero with a rate depending on the power exponent of the lower term.

DOI: https://doi.org/10.4213/sm638

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English version:
Sbornik: Mathematics, 2002, 193:3, 409–422

Bibliographic databases:

UDC: 517.95
MSC: Primary 35B27; Secondary 35J60
Received: 27.12.2000

Citation: H. Matevossian, S. V. Pikulin, “On the homogenization of semilinear elliptic operators in perforated domains”, Mat. Sb., 193:3 (2002), 101–114; Sb. Math., 193:3 (2002), 409–422

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. H. Matevossian, I. V. Filimonova, “On the averaging of weakly nonlinear parabolic operators in a perforated cylinder”, Russian Math. (Iz. VUZ), 49:9 (2005), 27–35  mathnet  mathscinet  elib
    2. H. Matevossian, I. V. Filimonova, “Homogenization of Semilinear Parabolic Operators in a Perforated Cylinder”, Math. Notes, 78:3 (2005), 364–374  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    3. Pikulin S.V., “Behavior of Solutions of Semilinear Elliptic Equations in Domains with Complicated Boundary”, Russ. J. Math. Phys., 19:3 (2012), 401–404  crossref  mathscinet  zmath  isi  elib  scopus  scopus  scopus
    4. S. V. Pikulin, “Ob otsenke razmera zony lokalizatsii nositelya resheniya polulineinogo ellipticheskogo uravneniya”, Vestn. SamGU. Estestvennonauchn. ser., 2013, no. 9/1(110), 28–34  mathnet
    5. S. V. Pikulin, “Convergence of a family of solutions to a Fujita-type equation in domains with cavities”, Comput. Math. Math. Phys., 56:11 (2016), 1872–1900  mathnet  crossref  crossref  isi  elib
  • Математический сборник - 1992–2005 Sbornik: Mathematics (from 1967)
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