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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. Travelling waves for detonations reduce to
specific heteroclinic orbits of a discontinuous system of ODE's.
The existence proof for heteroclinic orbits corresponding to weak
and strong detonation waves is carried out by some general
topological arguments in ODE. The nonuniqueness of these waves are
also considered.
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