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Tr. Mat. Inst. Steklova, 2010, Volume 270, Pages 266–280 (Mi tm3022)  

This article is cited in 7 scientific papers (total in 7 papers)

Correctors for some asymptotic problems

Michel Chipot, Senoussi Guesmia

Institute of Mathematics, University of Zürich, Zürich, Switzerland

Abstract: In the theory of anisotropic singular perturbation boundary value problems, the solution $u_\varepsilon$ does not converge, in the $H^1$-norm on the whole domain, towards some $u_0$. In this paper we construct correctors to have good approximations of $u_\varepsilon$ in the $H^1$-norm on the whole domain. Since the anisotropic singular perturbation problems can be connected to the study of the asymptotic behaviour of problems defined in cylindrical domains becoming unbounded in some directions, we transpose our results for such problems.

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English version:
Proceedings of the Steklov Institute of Mathematics, 2010, 270, 263–277

Bibliographic databases:

UDC: 517.95
Received in March 2009
Language:

Citation: Michel Chipot, Senoussi Guesmia, “Correctors for some asymptotic problems”, Differential equations and dynamical systems, Collected papers, Tr. Mat. Inst. Steklova, 270, MAIK Nauka/Interperiodica, Moscow, 2010, 266–280; Proc. Steklov Inst. Math., 270 (2010), 263–277

Citation in format AMSBIB
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\paper Correctors for some asymptotic problems
\inbook Differential equations and dynamical systems
\bookinfo Collected papers
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\vol 270
\pages 266--280
\publ MAIK Nauka/Interperiodica
\publaddr Moscow
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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. Chipot M., Guesmia S., “On a class of integro-differential problems”, Commun. Pure Appl. Anal., 9:5 (2010), 1249–1262  crossref  mathscinet  zmath  isi  scopus
    2. Guesmia S., Sengouga A., “Anisotropic singular perturbations of hyperbolic problems”, Appl. Math. Comput., 217:22 (2011), 8983–8996  crossref  mathscinet  zmath  isi  scopus
    3. Chipot M., Guesmia S., “On some anisotropic, nonlocal, parabolic singular perturbations problems”, Appl. Anal., 90:12 (2011), 1775–1789  crossref  mathscinet  zmath  isi  scopus
    4. Guesmia S., Sengouga A., “Some Singular Perturbations Results for Semilinear Hyperbolic Problems”, Discret. Contin. Dyn. Syst.-Ser. S, 5:3 (2012), 567–580  crossref  mathscinet  zmath  isi  scopus
    5. Guesmia S., Kechkar R., Moulay M.S., “Existence Results for Some Partial Integro-Differential Equations”, Mediterr. J. Math., 13:6 (2016), 4063–4079  crossref  mathscinet  zmath  isi  scopus
    6. Azouz S., Guesmia S., “Asymptotic development of anisotropic singular perturbation problems”, Asymptotic Anal., 100:3-4 (2016), 131–152  crossref  mathscinet  zmath  isi  scopus
    7. Guesmia S., Harkat S., “Long Time Behaviour of Parabolic Equations in Time-Dependent Growing Domains”, Asymptotic Anal., 108:4 (2018), 187–219  crossref  mathscinet  zmath  isi  scopus
  • Труды Математического института им. В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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