On the structure of the spectra for a class of combustion waves

Peter L. Simon, Stephen K. Scott, Serafim Kalliadasis, John H. Merkin

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3 Citations (Scopus)


The stability of a premixed laminar flame supported by a general combustion reaction system is considered using the Evans function method. The spectrum of the linearised second-order differential operator is investigated in detail. The special structure of the differential equations due to an Arrhenius temperature dependence is exploited. It is shown that, for certain combustion systems, the limit of the Jacobian of the reaction terms as the travelling wave coordinate approaches the front and rear of the flame is a lower triangular matrix. For this type of system a simple geometrical method is shown for the study of the essential spectrum of the linearised operator, and for determining the domain of the Evans function. The results are applied to some representative combustion reactions.

Original languageEnglish
Pages (from-to)309-328
Number of pages20
JournalJournal of Mathematical Chemistry
Issue number4
Publication statusPublished - Apr 1 2004



  • Evans function
  • travelling wave

ASJC Scopus subject areas

  • Chemistry(all)
  • Applied Mathematics

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