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Paper IPM / M / 508  


Abstract:  
The existence of travelling wave solution 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 CJ detonation reduce to finding specific heteroclinic orbits of a discontinuous system of ODE's; this heteroclinic orbits connect a rest point
corresponding to unburnt state to that of the burnt state. The existence proof for heteroclinic orbits corresponding to CJ detonation waves is carried out by some general topological arguments in ODE.
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