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Front propagation in reaction-dispersal with anomalous distributions

  • V. Méndez
  • V. Ortega-Cejas
  • J. Casas-Vázquez
Statistical and Nonlinear Physics

Abstract.

The speed of pulled fronts for parabolic fractional-reaction-dispersal equations is derived and analyzed. From the continuous-time random walk theory we derive these equations by considering long-tailed distributions for waiting times and dispersal distances. For both cases we obtain the corresponding Hamilton-Jacobi equation and show that the selected front speed obeys the minimum action principle. We impose physical restrictions on the speeds and obtain the corresponding conditions between a dimensionless number and the fractional indexes.

PACS.

05.40.Fb Random walks and Levy flights 05.60.Cd Classical transport 82.40.-g Chemical kinetics and reactions: special regimes and techniques 

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References

  1. R. Metzler, J. Klafter, Phys. Rep. 339, 1 (2000) MATHMathSciNetCrossRefADSGoogle Scholar
  2. S. Fedotov, V. Méndez, Phys. Rev. E 66, 030102(R) (2002) MathSciNetCrossRefADSGoogle Scholar
  3. B.I. Henry, S.L. Wearne, Physica A 276, 448 (2000); B.I. Henry, S.L. Wearne, SIAM J. Appl. Math. 62, 870 (2002) MathSciNetCrossRefADSGoogle Scholar
  4. D. del-Castillo-Negrete, B.A. Carreras, V.E. Lynch, Phys. Rev. Lett. 91, 018302 (2003); R. Mancinelli, D. Vergni, A. Vulpiani, Europhys. Lett. 60, 532 (2002) CrossRefADSGoogle Scholar
  5. J.D. Murray, Mathematical Biology (Springer-Verlag, New-York, 1989) Google Scholar
  6. M. Freidlin, Markov Processes and Differential Equations: Asymptotic Problems (Birkhauser, Basel, 1996) Google Scholar
  7. G.M. Zaslavsky, Phys. Rep. 371, 461 (2002) MATHMathSciNetCrossRefADSGoogle Scholar
  8. S.G. Samko, A.A. Kilbas, O.I. Marichev, Fractional Integrals and Derivatives (Gordon and Breach Science Publishers, Switzerland, 1993) Google Scholar
  9. A.V. Chechkin, R. Gorenflo, I.M. Sokolov, Phys. Rev. E 66, 0461292 (2002) CrossRefGoogle Scholar
  10. S. Fedotov, Phys. Rev. Lett. 86, 926 (2001) MathSciNetCrossRefADSGoogle Scholar
  11. M. Ciesielski, J. Leszczynski, e-print arXiv:math-ph/0309007 Google Scholar
  12. V.E. Lynch, B.A. Carreras, D. del Castillo-Negrete, K.M. Ferreiras-Mejías, H.R. Hicks, J. Comput. Phys. 192, 406 (2003) MATHMathSciNetCrossRefADSGoogle Scholar
  13. I.M. Sokolov, M.G. Schmidt, F. Sagués, Phys. Rev. E 73, 031102 (2006) CrossRefADSGoogle Scholar

Copyright information

© EDP Sciences/Società Italiana di Fisica/Springer-Verlag 2006

Authors and Affiliations

  • V. Méndez
    • 1
  • V. Ortega-Cejas
    • 1
  • J. Casas-Vázquez
    • 1
  1. 1.Grup de Física Estadística, Departament de FísicaFacultat de CiènciesBellaterraSpain

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