A study of traveling waves in subsonic detonation which describes combustion in porous media. An analytical resolution of the issue of uniqueness of the wave in the presence od non-zero diffusivity using geometric singular perturbation theory.

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 reaction front propagating with a well defined speed. It is known that traveling waves exist for any value of thermal diffusivity. 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. We analytically resolve the issue of uniqueness of the wave in the presence of non-zero diffusivity through applying geometric singular perturbation theory.
Co-authors: C.K.R.T. Jones (UNC-Chapel Hill), and P. Gordon (NJIT).

Keywords:

Traveling waves; combustion; perturbation theory.

Lecture #13235

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