Existence of global BV solutions to a model of reacting Euler fluid with variable thermodynamics parameters

We investigate the Cauchy problems of Euler equations coupled with chemical reaction equation. The specific heat and adiabatic parameters of compressible fluid are introduced as functions with respect to reactant mass fraction in this paper. By means of fractional step wave-front tracking scheme, we derive the existence of global BV solution, and verify that it is indeed an entropy weak solution. This system is also regarded as balance law with resonant characteristic fields. Hence some decay condition is imposed on the source term, in order to handle the damping effect.