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

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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.

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Authors and Affiliations

  1. Department of Mathematics, University of North Carolina, Chapel Hill, NC, 27599, USA

    Anna Ghazaryan & Christopher K. R. T. Jones

  2. Department of Mathematical Sciences, New Jersey Institute of Technology, Newark, NJ, 07102, USA

    Peter Gordon

Authors
  1. Anna Ghazaryan
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  2. Peter Gordon
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  3. Christopher K. R. T. Jones
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Correspondence to Anna Ghazaryan.

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Dedicated to Mr. Brunovsky in honor of his 70th birthday.

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Ghazaryan, A., Gordon, P. & Jones, C.K.R.T. Traveling Waves in Porous Media Combustion: Uniqueness of Waves for Small Thermal Diffusivity. J Dyn Diff Equat 19, 951–966 (2007). https://doi.org/10.1007/s10884-007-9079-9

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  • DOI: https://doi.org/10.1007/s10884-007-9079-9

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