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Title: Gevrey properties of the asymptotic critical wave speed in scalar reaction-diffusion equations
Authors: De Maesschalck, Peter
Popovic, Nikola
Issue Date: 2012
Abstract: 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 series 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 the 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. Popovi ´ c, T.J. Kaper, The asymptotic critical wave speed in a family of scalar reaction–diffusion equations, J. Math. Anal. Appl. 326 (2) (2007) 1007–1023], and makes use of the blow-up technique in combination with geometric singular perturbation theory and complex analysis, while the numerical evaluation of the coefficients in the expansion for the critical speed is based on rigorous interval arithmetic.
URI: http://hdl.handle.net/1942/13229
DOI: 10.1016/j.jmaa.2011.08.016
ISI #: 000295563500005
ISSN: 0022-247X
Category: A1
Type: Journal Contribution
Validation: ecoom, 2012
Appears in Collections: Research publications

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