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http://hdl.handle.net/1942/4043
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DC Field | Value | Language |
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dc.contributor.author | DUMORTIER, Freddy | - |
dc.contributor.author | Popovic, Nikola | - |
dc.contributor.author | Kaper, Tasso J. | - |
dc.date.accessioned | 2007-12-07T15:01:34Z | - |
dc.date.available | 2007-12-07T15:01:34Z | - |
dc.date.issued | 2007 | - |
dc.identifier.citation | JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 326(2). p. 1007-1023 | - |
dc.identifier.issn | 0022-247X | - |
dc.identifier.uri | http://hdl.handle.net/1942/4043 | - |
dc.description.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. | - |
dc.language.iso | en | - |
dc.publisher | ACADEMIC PRESS INC ELSEVIER SCIENCE | - |
dc.subject.other | reaction-diffusion equations; traveling waves; critical wave speeds; asymptotic expansions; blow-up technique | - |
dc.title | The asymptotic critical wave speed in a family of scalar reaction-diffusion equations | - |
dc.type | Journal Contribution | - |
dc.identifier.epage | 1023 | - |
dc.identifier.issue | 2 | - |
dc.identifier.spage | 1007 | - |
dc.identifier.volume | 326 | - |
local.format.pages | 17 | - |
local.bibliographicCitation.jcat | A1 | - |
dc.description.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 | - |
local.type.refereed | Refereed | - |
local.type.specified | Article | - |
dc.bibliographicCitation.oldjcat | A1 | - |
dc.identifier.doi | 10.1016/j.jmaa.2006.03.050 | - |
dc.identifier.isi | 000242816300019 | - |
item.accessRights | Closed Access | - |
item.fulltext | No Fulltext | - |
item.validation | ecoom 2008 | - |
item.contributor | DUMORTIER, Freddy | - |
item.contributor | Popovic, Nikola | - |
item.contributor | Kaper, Tasso J. | - |
item.fullcitation | DUMORTIER, Freddy; Popovic, Nikola & Kaper, Tasso J. (2007) The asymptotic critical wave speed in a family of scalar reaction-diffusion equations. In: JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 326(2). p. 1007-1023. | - |
crisitem.journal.issn | 0022-247X | - |
crisitem.journal.eissn | 1096-0813 | - |
Appears in Collections: | Research publications |
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