Fronts in Reactive Convection: Bounds, Stability, and Instability

Peter Constantin, Alexander Kiselev, Lenya Ryzhik

Research output: Contribution to journalArticlepeer-review

17 Scopus citations


This paper examines a simplified active combustion model in which the reaction influences the flow. We consider front propagation in a reactive Boussinesq system in an infinite vertical strip. Nonlinear stability of planar fronts is established for narrow domains when the Rayleigh number is not too large. Planar fronts are shown to be linearly unstable with respect to long-wavelength perturbations if the Rayleigh number is sufficiently large. We also prove uniform bounds on the bulk burning rate and the Nusselt number in the KPP reaction case.

Original languageEnglish (US)
Pages (from-to)1781-1803
Number of pages23
JournalCommunications on Pure and Applied Mathematics
Issue number12
StatePublished - Dec 2003
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • General Mathematics
  • Applied Mathematics


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