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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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Linking options:
http://mi.mathnet.ru/eng/msb638https://doi.org/10.4213/sm638 http://mi.mathnet.ru/eng/msb/v193/i3/p101
Citing articles on Google Scholar:
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Russian articles,
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This publication is cited in the following articles:
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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
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H. Matevossian, I. V. Filimonova, “Homogenization of Semilinear Parabolic Operators in a Perforated Cylinder”, Math. Notes, 78:3 (2005), 364–374
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Pikulin S.V., “Behavior of Solutions of Semilinear Elliptic Equations in Domains with Complicated Boundary”, Russ. J. Math. Phys., 19:3 (2012), 401–404
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S. V. Pikulin, “Ob otsenke razmera zony lokalizatsii nositelya resheniya polulineinogo ellipticheskogo uravneniya”, Vestn. SamGU. Estestvennonauchn. ser., 2013, no. 9/1(110), 28–34
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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
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