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On the existence of Chapman-Jouguet detonation waves

Published online by Cambridge University Press:  17 April 2009

Mahmoud Hesaaraki  and
Abdolrahman Razani
Mahmoud Hesaaraki
Affiliation:
Department of Mathematics, Sharif University of Technology, P.O. Box 11365–9415, Tehran, Iran, e-mail: hesaraki@math.sharif.ac.ir
Abdolrahman Razani
Affiliation:
Department of Mathematics, Faculty of Science, Tarbiat Modarres University, P.O. Box 14155–4838, Tehran, Iran, e-mail: razani@karun.ipm.ac.ir, detwave@vax.ipm.ac.ir
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Abstract

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The existence of travelling wave solutions to equations of a viscous, heat-conducting combustible fluid is proved. The reactions are assumed to be one step exothermic reactions with a natural discontinuous reaction rate function. The problem is studied for a general gas. Instead of assuming the ideal gas conditions we consider a general thermodynamics which is described by a fairly mild set of hypotheses. The existence proof of travelling waves for Chapman-Jouguet detonation reduces to finding specific heteroclinic orbits of a discontinuous system of ordinary differential equations: these heteroclinic orbits connect a rest point corresponding to unburnt state to that of the burnt state. The existence proof for heteroclinic orbits corresponding to Chapman-Jouguet detonation waves is carried out by some general topological arguments in ordinary differential equations theory.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 63 , Issue 3 , June 2001 , pp. 485 - 496
Copyright
Copyright © Australian Mathematical Society 2001

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