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New type of travelling wave solutions
Author(s) -
Schneider K. R.,
Shchepakina E. A.,
Sobolev V. A.
Publication year - 2003
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.404
Subject(s) - traveling wave , mathematics , adiabatic process , type (biology) , explosive material , combustion , autocatalysis , mathematical analysis , classical mechanics , mechanics , physics , thermodynamics , chemistry , geology , paleontology , organic chemistry , kinetics
We study the existence of combustion waves for an autocatalytic reaction in the non‐adiabatic case. Based on the fact that the reaction system has canard solutions separating the slow combustion regime from the explosive one, we prove by applying the geometric theory of singularly perturbed differential equations the existence of a new type of travelling waves solutions, the so‐called canard travelling waves. Copyright © 2003 John Wiley & Sons, Ltd.