Advertisement

Applied Mathematics & Optimization

, Volume 78, Issue 2, pp 329–359 | Cite as

On a Dual Formulation for Growing Sandpile Problem with Mixed Boundary Conditions

  • N. Igbida
  • F. Karami
  • S. Ouaro
  • U. Traoré
Article
  • 73 Downloads

Abstract

In this work, we introduce and study a Prigozhin model for growing sandpile with mixed boundary conditions. For theoretical analysis we use semi-group theory and the numerical part is based on a duality approach.

Keywords

Sandpile Mixed boundary conditions Subdifferential operator Nonlinear semigroup dual formulation Numerical approximation 

References

  1. 1.
    Ambrosio, L.: Lecture notes on optimal transport, in mathematical aspect of evolving interfaces. Lecture Notes in Mathematics, vol. 1812. Springer, Berlin (2003)Google Scholar
  2. 2.
    Barrett, J.W., Prigozhin, L.: A mixed formulation for the Monge–Kantorovich equations. M2AN 41(6), 1041–1060 (2007)MathSciNetCrossRefGoogle Scholar
  3. 3.
    Barrett, J.W., Prigozhin, L.: Dual Formulation in critical state problems. Interfaces Free Bound. 8, 349–370 (2006)MathSciNetCrossRefGoogle Scholar
  4. 4.
    Brezis. H.: Opérateurs maximaux monotones et semi-groupes de contractions dans les espaces de Hilbert. (French). North-Holland Mathematics Studies, No. 5. Notas de Matemàtica (50). North-Holland Publishing Co., Amsterdam-London; American Elsevier Publishing Co., Inc., New York 1973 (1987)Google Scholar
  5. 5.
    Dumont, S., Igbida, N.: On a dual formulation for growing sandpile problem. Eur. J. Appl. Math. 20(2), 169–185 (2009)MathSciNetCrossRefGoogle Scholar
  6. 6.
    Dumont, S., Igbida, N.: On the collapsing sandpile problem. Commun. Pure Appl. Anal. 10(2), 625–638 (2011)MathSciNetCrossRefGoogle Scholar
  7. 7.
    Ekeland, I., Témam, R.: Convex analysis and variational problems. In: Classics in Applied mathematics, vol. 28. Society for Industrial and Applied Mathematics (SIAM), Philadelphia (1999)Google Scholar
  8. 8.
    Evans, L.C.: Partial differential equations and Monge-Kantorovich mass transfert. Current Developments in Mathematics, pp. 65–126. International Press, Bostan (1997)Google Scholar
  9. 9.
    Evans, L.C.: Partial Differential Equations. Graduate Studies in Mathematics, vol. 19. American Mathematical Society, Providence (1998)Google Scholar
  10. 10.
    Evans, L.C., Gangbo, W.: Differential equations methods for the Monge–Kantorovich mass transfert problem. Mem. Am. Math. Soc. 137, 653 (1999)zbMATHGoogle Scholar
  11. 11.
    Lions, J.L.: Quelques methodes de résolution des problèmes aux limites non linéaires. Dunod, Gauthier-Villars, Paris (1996)zbMATHGoogle Scholar
  12. 12.
    Prigozhin, L.: Variational model of sandpile growth. Eur. J. App. Math. 7, 225–236 (1996)MathSciNetzbMATHGoogle Scholar
  13. 13.
    Roberts, J.E., Thomas, J.M.: Mixed and hybrid methods. In: Ciarlet, P.G., Lions, J.L. (eds.) Handbook of Numerical Analysis, Finite Element Methods (Part1), vol. II. North-Holland, Amsterdam (1991)Google Scholar

Copyright information

© Springer Science+Business Media New York 2017

Authors and Affiliations

  1. 1.Institut de Recherche XLIM-DMI, UMR-CNRS 7252, Faculté des Sciences et TechniquesUniversité de LimogesLimogesFrance
  2. 2.Institut de Recherche XLIM-DMI, UMR-CNRS 7252, Faculté des Sciences et TechniquesUniversité Cadi AyyadEssaouira El JadidaMorocco
  3. 3.LAboratoire de Mathématiques et Informatique (LAMI), UFR, Sciences Exactes et AppliquéesUniversité Ouaga I Pr Joseph Ki-ZerboOuagadougouBurkina Faso

Personalised recommendations