Please use this identifier to cite or link to this item: http://hdl.handle.net/1942/4043
Title: The asymptotic critical wave speed in a family of scalar reaction-diffusion equations
Authors: DUMORTIER, Freddy 
Popovic, Nikola
Kaper, Tasso J.
Issue Date: 2007
Publisher: ACADEMIC PRESS INC ELSEVIER SCIENCE
Source: JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 326(2). p. 1007-1023
Abstract: We study traveling wave solutions for the class of scalar reaction-diffusion equations au/at = a(2)u/ax(2) + f(m)(u), where the family of potential functions {f(m)} is given by f(m)(u) = 2u(m) (1 - u). For each m >= 1 real, there is a critical wave speed C-crit(m) that separates waves of exponential structure from those which decay only algebraically. We derive a rigorous asymptotic expansion for c(crit)(m) in the limit as m -> infinity. This expansion also seems to provide a useful approximation to ccrit(m) over a wide range of m-values. Moreover, we prove that c(crit)(m) is C-infinity-smooth as a function of m(-1). Our analysis relies on geometric singular perturbation theory, as well as on the blow-up technique, and confirms the results obtained by means of asymptotic methods in [D.J. Needham, A.N. Barries, Reaction-diffusion and phase waves occurring in a class of scalar reaction-diffusion equations, Nonlinearity 12 (1) (1999) 41-58; T.P. Witelski, K. Ono, T.J. Kaper, Critical wave speeds for a family of scalar reaction-diffusion equations, Appl. Math. Lett. 14 (1) (2001) 65-73]. (c) 2006 Elsevier Inc. All rights reserved.
Notes: Boston Univ, Ctr Ciodynam, Boston, MA 02215 USA. Boston Univ, Dept Math & Stat, Boston, MA 02215 USA. Univ Hasselt, B-3590 Diepenbeek, Belgium.Popovic, M, Boston Univ, Ctr Ciodynam, Boston, MA 02215 USA.freddy.dumortier@uhasselt.be popovic@math.bu.edu tasso@math.bu.edu
Keywords: reaction-diffusion equations; traveling waves; critical wave speeds; asymptotic expansions; blow-up technique
Document URI: http://hdl.handle.net/1942/4043
ISSN: 0022-247X
e-ISSN: 1096-0813
DOI: 10.1016/j.jmaa.2006.03.050
ISI #: 000242816300019
Category: A1
Type: Journal Contribution
Validations: ecoom 2008
Appears in Collections:Research publications

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