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Gevrey properties of the asymptotic critical wave speed in a family of scalar reaction-diffusion equations

© INRIA Sophie Auvin - S comme Simulation

Entrée libre, 14h30.

  • Date : 4/05/2011
  • Lieu : Inria Rocquencourt, salle de réunion du bâtiment 16
  • Intervenant(s) : Nikola Popovic (School of Mathematics, University of Edinburgh)
  • Organisateur(s) : Equipe Sisyphe

We consider front propagation in a family of scalar reaction-diffusion equations in the asymptotic limit where the polynomial degree of the potential function tends to infinity. We investigate the Gevrey properties of the corresponding critical propagation speed, proving that the formal asymptotic expansion for that speed is Gevrey-1 with respect to the inverse of the degree. Moreover, we discuss the question of optimal truncation. Finally, we present a reliable numerical algorithm for evaluating the coefficients in that expansion with arbitrary precision and to any desired order, and we illustrate that algorithm by calculating explicitly the first ten coefficients. Our analysis builds on results obtained previously in [F. Dumortier, N. Popovic, and T.J. Kaper, The asymptotic critical wave speed in a family of scalar reaction-diffusion equations. J. Math. Anal. Appl., 326(2): 1007–1023, 2007], and makes use of the blow-up technique in combination with geometric singular perturbation theory and complex analysis, while the numerical computation of the coefficients in the expansion for the critical speed is based on rigorous interval arithmetics.

Mots-clés : SISYPHE Paris - Rocquencourt

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