Travelling fronts in pressure-driven combustion

Fathi Dkhil and Karl Peter Hadeler

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Submission date: 25. Jun. 2004
published in: SIAM journal on applied mathematics, 66 (2006) 5, p. 1473-1481 
DOI number (of the published article): 10.1137/040611148
Bibtex
MSC-Numbers: 35K55, 35K57, 37C29, 76L05, 80A25
Keywords and phrases: combustion, deflagration, travelling front, reaction diffusion

Abstract:
Brailovsky and Sivashinsky have proposed a model for pressure-driven combustion in the form of a degenerate parabolic system for temperature, concentration and pressure. it is shown that the existence and uniqueness problem for travelling front solutions can be completely solved by exploiting the existing invariants and phase plane methods. The approach yields travelling fronts for a variety of related problems which are interpreted in physical terms.