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Matematicheskie Zametki, 2005, Volume 78, Issue 3, Pages 396–408
DOI: https://doi.org/10.4213/mzm2596 (Mi mzm2596) 		 
This article is cited in 4 scientific papers (total in 4 papers)

Homogenization of Semilinear Parabolic Operators in a Perforated Cylinder

H. Matevossian, I. V. Filimonova

M. V. Lomonosov Moscow State University
Full-text PDF (237 kB) Citations (4)
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DOI: https://doi.org/10.4213/mzm2596
Abstract: In this paper, we consider a semilinear parabolic equation of second order with lower term a power function of the unknown function and prove that the sequence of solutions in a perforated cylinder tends to a solution in a unperforated cylinder if the radii of rejected balls in the parabolic metric tend to zero at the rate depending on the exponent of the power function in the lower term.
Received: 09.06.2003
English version:
Mathematical Notes, 2005, Volume 78, Issue 3, Pages 364–374
DOI: https://doi.org/10.1007/s11006-005-0135-7
Bibliographic databases:
UDC: 517.95
Language: Russian
Citation: H. Matevossian, I. V. Filimonova, “Homogenization of Semilinear Parabolic Operators in a Perforated Cylinder”, Mat. Zametki, 78:3 (2005), 396–408; Math. Notes, 78:3 (2005), 364–374
Citation in format AMSBIB
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\pages 396--408
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  • https://www.mathnet.ru/eng/mzm2596
  • https://doi.org/10.4213/mzm2596
  • https://www.mathnet.ru/eng/mzm/v78/i3/p396
    • This publication is cited in the following 4 articles:
    1. Hovik A. Matevossian, Giorgio Nordo, “Homogenization of the Semi-linear Parabolic Problem in a Perforated Cylinder”, Lobachevskii J Math, 43:7 (2022), 1934  crossref
    2. 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
    3. T. A. Mel'nik, O. A. Sivak, “Asymptotic approximations for solutions to quasilinear and linear parabolic problems with different perturbed boundary conditions in perforated domains”, J Math Sci, 177:1 (2011), 50  crossref
    4. T. A. Mel'nik, O. A. Sivak, “Asymptotic analysis of a parabolic semilinear problem with nonlinear boundary multiphase interactions in a perforated domain”, J Math Sci, 164:3 (2010), 427  crossref
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Математические заметки Mathematical Notes
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