WIAS Preprint No. 694, (2001)

A new type of travelling wave solutions


  • Schneider, Klaus R.
  • Shchepakina, Elena
  • Sobolev, Vladimir

2010 Mathematics Subject Classification

  • 34E15 35B25 35K55 80A25


  • travelling wave, singular perturbations, canards, combustion


We study the existence of combustion waves for an autocatalytic reaction in the non-adiabatic case. Basing 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.

Appeared in

  • Math. Methods Appl. Sci., 26 (2003), 1349-1361

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