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Journal of Dynamics and Differential Equations

, Volume 19, Issue 4, pp 951–966 | Cite as

Traveling Waves in Porous Media Combustion: Uniqueness of Waves for Small Thermal Diffusivity

  • Anna Ghazaryan
  • Peter Gordon
  • Christopher K. R. T. Jones
Article

We study traveling wave solutions arising in Sivashinsky’s model of subsonic detonation which describes combustion processes in inert porous media. Subsonic (shockless) detonation waves tend to assume the form of a reaction front propagating with a well defined speed. It is known that traveling waves exist for any value of thermal diffusivity [5]. Moreover, it has been shown that, when the thermal diffusivity is neglected, the traveling wave is unique. The question of whether the wave is unique in the presence of thermal diffusivity has remained open. For the subsonic regime, the underlying physics might suggest that the effect of small thermal diffusivity is insignificant. We analytically prove the uniqueness of the wave in the presence of non-zero diffusivity through applying geometric singular perturbation theory.

Keywords

Geometric singular perturbation theory traveling waves subsonic detonation porous media combustion 

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References

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Copyright information

© Springer Science+Business Media, LLC 2007

Authors and Affiliations

  • Anna Ghazaryan
    • 1
  • Peter Gordon
    • 2
  • Christopher K. R. T. Jones
    • 1
  1. 1.Department of MathematicsUniversity of North CarolinaChapel HillUSA
  2. 2.Department of Mathematical SciencesNew Jersey Institute of TechnologyNewarkUSA

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