Traveling Waves in Porous Media Combustion: Uniqueness of Waves for Small Thermal Diffusivity |
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Authors: | Anna Ghazaryan Peter Gordon Christopher K R T Jones |
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Institution: | (1) Department of Mathematics, University of North Carolina, Chapel Hill, NC 27599, USA;(2) Department of Mathematical Sciences, New Jersey Institute of Technology, Newark, NJ 07102, USA |
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Abstract: | 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.
Dedicated to Mr. Brunovsky in honor of his 70th birthday. |
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Keywords: | Geometric singular perturbation theory traveling waves subsonic detonation porous media combustion |
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