Traveling waves in porous media combustion: Uniqueness of waves for small thermal diffusivity

Document Type

Article

Publication Date

12-1-2007

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. © 2007 Springer Science+Business Media, LLC.

Identifier

36549045138 (Scopus)

Publication Title

Journal of Dynamics and Differential Equations

External Full Text Location

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

e-ISSN

15729222

ISSN

10407294

First Page

951

Last Page

966

Issue

4

Volume

19

Grant

DMS-0554775

Fund Ref

National Science Foundation

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