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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2010, Volume 270, Pages 266–280 (Mi tm3022)  
This article is cited in 13 scientific papers (total in 13 papers)

Correctors for some asymptotic problems

Michel Chipot, Senoussi Guesmia

Institute of Mathematics, University of Zürich, Zürich, Switzerland
Full-text PDF (57 kB) Citations (13)
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Abstract: In the theory of anisotropic singular perturbation boundary value problems, the solution uε does not converge, in the H1-norm on the whole domain, towards some u0. In this paper we construct correctors to have good approximations of uε in the H1-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.
Received in March 2009
English version:
Proceedings of the Steklov Institute of Mathematics, 2010, Volume 270, Pages 263–277
DOI: https://doi.org/10.1134/S0081543810030211
Bibliographic databases:
Document Type: Article
UDC: 517.95
Language: English
Citation: Michel Chipot, Senoussi Guesmia, “Correctors for some asymptotic problems”, Differential equations and dynamical systems, Collected papers, Trudy 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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  • https://www.mathnet.ru/eng/tm3022
  • https://www.mathnet.ru/eng/tm/v270/p266
    • This publication is cited in the following 13 articles:
    1. Yahiaoui A., Guesmia S., Sengouga A., “Anisotropic Non-Local Problems: Asymptotic Behaviour and Existence Results”, Complex Var. Elliptic Equ., 67:5 (2022), 1121–1153  crossref  mathscinet  isi  scopus
    2. Bunoiu R., Cardone G., Kengne R., Woukeng J.L., “Homogenization of 2D Cahn-Hilliard-Navier-Stokes System”, J. Elliptic Parabol. Equat., 6:1 (2020), 377–408  crossref  mathscinet  isi
    3. Chekroun M.D., Hong Y., Temam R.M., “Enriched Numerical Scheme For Singularly Perturbed Barotropic Quasi-Geostrophic Equations”, J. Comput. Phys., 416 (2020), 109493  crossref  mathscinet  isi
    4. Ceccaldi A., Mardare S., “On Correctors to Elliptic Problems in Long Cylinders”, J. Elliptic Parabol. Equat., 5:2 (2019), 473–491  crossref  mathscinet  isi
    5. 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
    6. 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
    7. Azouz S., Guesmia S., “Asymptotic development of anisotropic singular perturbation problems”, Asymptotic Anal., 100:3-4 (2016), 131–152  crossref  mathscinet  zmath  isi  scopus
    8. Michel Chipot, “ℓ GOES TO PLUS INFINITY : AN UPDATE”, Journal of the Korea Society for Industrial and Applied Mathematics, 18:2 (2014), 107  crossref
    9. 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
    10. Guesmia S., Sengouga A., “Anisotropic singular perturbations of hyperbolic problems”, Appl. Math. Comput., 217:22 (2011), 8983–8996  crossref  mathscinet  zmath  isi  scopus
    11. Chipot M., Guesmia S., “On some anisotropic, nonlocal, parabolic singular perturbations problems”, Appl. Anal., 90:12 (2011), 1775–1789  crossref  mathscinet  zmath  isi  scopus
    12. M. Chipot, S. Guesmia, A. Sengouga, “Singular perturbations of some nonlinear problems”, J Math Sci, 176:6 (2011), 828  crossref
    13. 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
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    		Труды Математического института имени В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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