Comptes Rendus
Partial Differential Equations
Exponential rates of convergence by an iteration technique
[Convergences exponentielles par une technique itérative]
Comptes Rendus. Mathématique, Volume 346 (2008) no. 1-2, pp. 21-26.

The goal of this Note is to introduce a technique leading to a convergence of exponential type for the solution of problems set in cylinders becoming unbounded in some directions.

Le but de cette Note est la présentation d'une technique conduisant à une convergence de type exponentiel pour la solution de problèmes posés dans des cylindres dont certaines directions tendent vers l'infini.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2007.12.004

Michel Chipot 1 ; Karen Yeressian 1

1 Institute of Mathematics, University of Zürich, Winterthurerstrasse 190, CH-8057 Zurich, Switzerland
@article{CRMATH_2008__346_1-2_21_0,
     author = {Michel Chipot and Karen Yeressian},
     title = {Exponential rates of convergence by an iteration technique},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {21--26},
     publisher = {Elsevier},
     volume = {346},
     number = {1-2},
     year = {2008},
     doi = {10.1016/j.crma.2007.12.004},
     language = {en},
}
TY  - JOUR
AU  - Michel Chipot
AU  - Karen Yeressian
TI  - Exponential rates of convergence by an iteration technique
JO  - Comptes Rendus. Mathématique
PY  - 2008
SP  - 21
EP  - 26
VL  - 346
IS  - 1-2
PB  - Elsevier
DO  - 10.1016/j.crma.2007.12.004
LA  - en
ID  - CRMATH_2008__346_1-2_21_0
ER  - 
%0 Journal Article
%A Michel Chipot
%A Karen Yeressian
%T Exponential rates of convergence by an iteration technique
%J Comptes Rendus. Mathématique
%D 2008
%P 21-26
%V 346
%N 1-2
%I Elsevier
%R 10.1016/j.crma.2007.12.004
%G en
%F CRMATH_2008__346_1-2_21_0
Michel Chipot; Karen Yeressian. Exponential rates of convergence by an iteration technique. Comptes Rendus. Mathématique, Volume 346 (2008) no. 1-2, pp. 21-26. doi : 10.1016/j.crma.2007.12.004. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2007.12.004/

[1] B. Brighi, S. Guesmia, On elliptic boundary value problems of order 2m in cylindrical domain of large size, in press

[2] M. Chipot Goes to Plus Infinity, Birkhäuser, 2002

[3] M. Chipot, S. Mardare, Asymptotic behaviour of the Stokes problem in cylinders becoming unbounded in one direction, in press

[4] M. Chipot; A. Rougirel On the asymptotic behavior of the solution of elliptic problems in cylindrical domains becoming unbounded, Commun. Contemp. Math., Volume 4 (2002) no. 1, pp. 15-24

[5] M. Chipot, K. Yeressian, in preparation

[6] M. Chipot; Y. Xie On the asymptotic behaviour of elliptic problems with periodic data, C. R. Acad. Sci. Paris, Ser. I, Volume 339 (2004), pp. 477-482

[7] M. Chipot; Y. Xie Elliptic problems with periodic data: an asymptotic analysis, J. Math. Pures Appl., Volume 85 (2006), pp. 345-370

[8] R. Dautray; J.L. Lions Mathematical Analysis and Numerical Methods for Science and Technology, Springer-Verlag, 1988

[9] D. Gilbarg; N.S. Trudinger Elliptic Partial Differential Equations of Second Order, Springer-Verlag, 1983

[10] S. Guesmia, Etude du comportement asymptotique de certaines équations aux dérivées partielles dans des domaines cylindriques, Thèse Université de Haute Alsace, December 2006

[11] Y. Xie, On Asymptotic Problems in Cylinders and Other Mathematical Issues, Thesis University of Zürich, May 2006

  • Luca Esposito; Prosenjit Roy; Firoj Sk On the asymptotic behavior of the eigenvalues of nonlinear elliptic problems in domains becoming unbounded, Asymptotic Analysis, Volume 123 (2021) no. 1-2, p. 79 | DOI:10.3233/asy-201626
  • Cristinel Mardare On the divergence problem in some particular domains, Journal of Elliptic and Parabolic Equations, Volume 6 (2020) no. 1, p. 257 | DOI:10.1007/s41808-020-00070-0
  • Adrien Ceccaldi; Sorin Mardare On correctors to elliptic problems in long cylinders, Journal of Elliptic and Parabolic Equations, Volume 5 (2019) no. 2, p. 473 | DOI:10.1007/s41808-019-00047-8
  • Adrien Ceccaldi Elliptic problems in long cylinders revisited, Ricerche di Matematica, Volume 68 (2019) no. 1, p. 265 | DOI:10.1007/s11587-018-0404-x
  • Michel Chipot; Stephanie Zube On the asymptotic behaviour of the pure Neumann problem in cylinder-like domains and its applications, Asymptotic Analysis, Volume 108 (2018) no. 3, p. 163 | DOI:10.3233/asy-181462
  • Senoussi Guesmia; Soumia Harkat Long time behaviour of parabolic equations in time-dependent growing domains, Asymptotic Analysis, Volume 108 (2018) no. 4, p. 187 | DOI:10.3233/asy-171461
  • Patrizia Donato; Sorin Mardare; Bogdan Vernescu Bingham Flows in Periodic Domains of Infinite Length, Chinese Annals of Mathematics, Series B, Volume 39 (2018) no. 2, p. 183 | DOI:10.1007/s11401-018-1059-3
  • Michel Chipot On Some Elliptic Problems in Unbounded Domains, Chinese Annals of Mathematics, Series B, Volume 39 (2018) no. 3, p. 597 | DOI:10.1007/s11401-018-0083-7
  • Indranil Chowdhury; Prosenjit Roy On the asymptotic analysis of problems involving fractional Laplacian in cylindrical domains tending to infinity, Communications in Contemporary Mathematics, Volume 19 (2017) no. 05, p. 1650035 | DOI:10.1142/s0219199716500358
  • Salima Azouz; Senoussi Guesmia Asymptotic development of anisotropic singular perturbation problems, Asymptotic Analysis, Volume 100 (2016) no. 3-4, p. 131 | DOI:10.3233/asy-161389
  • Ogabi Chokri On the Lp theory of Anisotropic singular perturbations of elliptic problems, Communications on Pure and Applied Analysis, Volume 15 (2016) no. 4, p. 1157 | DOI:10.3934/cpaa.2016.15.1157
  • Prosenjit Roy; Aleksandar Mojsic; Michel Chipot On some variational problems set on domains tending to infinity, Discrete and Continuous Dynamical Systems, Volume 36 (2016) no. 7, p. 3603 | DOI:10.3934/dcds.2016.36.3603
  • Michel Chipot; Sorin Mardare The Neumann problem in cylinders becoming unbounded in one direction, Journal de Mathématiques Pures et Appliquées, Volume 104 (2015) no. 5, p. 921 | DOI:10.1016/j.matpur.2015.05.008
  • Michel Chipot On The Asymptotic Behaviour of Some Problems of the Calculus of Variations, Journal of Elliptic and Parabolic Equations, Volume 1 (2015) no. 2, p. 307 | DOI:10.1007/bf03377383
  • Michel Chipot ℓ GOES TO PLUS INFINITY : AN UPDATE, Journal of the Korea Society for Industrial and Applied Mathematics, Volume 18 (2014) no. 2, p. 107 | DOI:10.12941/jksiam.2014.18.107
  • Senoussi Guesmia Large time and space size behaviour of the heat equation in non-cylindrical domains, Archiv der Mathematik, Volume 101 (2013) no. 3, p. 293 | DOI:10.1007/s00013-013-0555-7
  • Karen Yeressian; Michel Chipot On the asymptotic behavior of variational inequalities set in cylinders, Discrete and Continuous Dynamical Systems, Volume 33 (2013) no. 11/12, p. 4875 | DOI:10.3934/dcds.2013.33.4875
  • Senoussi Guesmia; Abdelmouhcene Sengouga Some singular perturbations results for semilinear hyperbolic problems, Discrete Continuous Dynamical Systems - S, Volume 5 (2012) no. 3, p. 567 | DOI:10.3934/dcdss.2012.5.567
  • Bibliography, Markov Processes, Semigroups and Generators (2010), p. 403 | DOI:10.1515/9783110250114.403
  • Michel Chipot; Senoussi Guesmia Correctors for some asymptotic problems, Proceedings of the Steklov Institute of Mathematics, Volume 270 (2010) no. 1, p. 263 | DOI:10.1134/s0081543810030211
  • Senoussi Guesmia Some convergence results for quasilinear parabolic boundary value problems in cylindrical domains of large size, Nonlinear Analysis: Theory, Methods Applications, Volume 70 (2009) no. 9, p. 3320 | DOI:10.1016/j.na.2008.04.036
  • Michel Chipot; Sorin Mardare Asymptotic behaviour of the Stokes problem in cylinders becoming unbounded in one direction, Journal de Mathématiques Pures et Appliquées, Volume 90 (2008) no. 2, p. 133 | DOI:10.1016/j.matpur.2008.04.002

Cité par 22 documents. Sources : Crossref

Commentaires - Politique