Numerical approximation of axisymmetric positive solutions of semilinear elliptic equations in axisymmetric domains of ℝ 3

N. Achtaich

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique (1997)

  • Volume: 31, Issue: 5, page 599-614
  • ISSN: 0764-583X

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Achtaich, N.. "Numerical approximation of axisymmetric positive solutions of semilinear elliptic equations in axisymmetric domains of $\mathbb {R}^3$." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 31.5 (1997): 599-614. <http://eudml.org/doc/193850>.

@article{Achtaich1997,
author = {Achtaich, N.},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},
keywords = {axisymmetric positive solutions; semilinear elliptic equations; nonlinear Poisson equation; variational methods; algorithm; numerical results},
language = {eng},
number = {5},
pages = {599-614},
publisher = {Dunod},
title = {Numerical approximation of axisymmetric positive solutions of semilinear elliptic equations in axisymmetric domains of $\mathbb \{R\}^3$},
url = {http://eudml.org/doc/193850},
volume = {31},
year = {1997},
}

TY - JOUR
AU - Achtaich, N.
TI - Numerical approximation of axisymmetric positive solutions of semilinear elliptic equations in axisymmetric domains of $\mathbb {R}^3$
JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
PY - 1997
PB - Dunod
VL - 31
IS - 5
SP - 599
EP - 614
LA - eng
KW - axisymmetric positive solutions; semilinear elliptic equations; nonlinear Poisson equation; variational methods; algorithm; numerical results
UR - http://eudml.org/doc/193850
ER -

References

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  2. [2] R. ADAMS, 1975, Sobolev spaces. Academic press. Zbl0314.46030MR450957
  3. [3] A. AMBROSETTI and P. H. RABINOWITZ, 1973, Dual variational methods in critical point. Theory and applications. Journal of functional Analysis, 14, 349-381. Zbl0273.49063MR370183
  4. [4] C. BANDLE and A. BRILLARD, 1994, Nonlinear elliptic equations involving critical Sobolev exponents : asymptotic analysis via methods of epi-convergence. Zeitschrift fur Analysis und ihre Anwendungen, Journal of analysis and its applications, Volume 13, n° 2, pp. 1-13. Zbl0808.35031MR1305597
  5. [5] H. BREZIS, 1983, Analyse fonctionnelle. Théorie et applications, Masson. Zbl0511.46001MR697382
  6. [6] H. BREZIS, 1986, Elliptic Equations with limiting Sobolev exponents. The impact of topology. Pure Appl Math., 39, pp. 17-39. Zbl0601.35043MR861481
  7. [7] H. BREZIS and L. NIRENBERG, 1983, Positive solutions of nonlinear elliptic equations involving critical Sobolev exponents. Comm. Pure Appl. Math., 36, pp. 437-477. Zbl0541.35029MR709644
  8. [8] P. G. CIARLET, 1982, Introduction à l'analyse numérique matricielle et à l'optimisation. Masson. Zbl0488.65001MR680778
  9. [9] J. M. CORON, 1984, Topologie et cas limite des injections de Sobolev. Cras Paris, t. 299, série I. Zbl0569.35032MR762722
  10. [10] I. EKLAND and R. TEMAM, 1973, Analyse convexe et problèmes variationnels. Dunod. Zbl0281.49001
  11. [11] J. L. LIONS, Quelques méthodes de résolution des problèmes aux limites non linéaires. Dunod (Paris 69). Zbl0189.40603
  12. [12] P. L. LIONS, 1982, On the existence of positive solutions of semilinear elliptic equations. SIAM Reviews 24, pp. 441-467. Zbl0511.35033MR678562
  13. [13] B. MERCIER and G. RAUGEL, 1982, Résolution d'un problème aux limites dans un ouvert axisymétrique par éléments finis en r, z et séries de Fourier en Θ. RAIRO (Analyse Numérique). Vol. 16. Zbl0531.65054MR684832
  14. [14] D. SERRE, Triplets de solutions d'une équation aux dérivées partielles elliptiques non linéaires. Lectures notes in Mathematics 782. Springer Verlag. Zbl0437.35002
  15. [15] F. de THELIN, 1984, Quelques résultats d'existence et de non existence pour une E.D.P. elliptique non linéaire. Cras Paris, t. 299, série I. Zbl0575.35030

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