Global entropy solutions to exothermically reacting, compressible Euler equations

The global existence of entropy solutions is established for the compressible Euler equations for one-dimensional or plane-wave flow of an ideal gas, which undergoes a one-step exothermic chemical reaction under Arrhenius-type kinetics. We assume that the reaction rate is bounded away from zero and the total variation of the initial data is bounded by a parameter that grows arbitrarily large as the equation of state converges to that of an isothermal gas. The heat released by the reaction causes the spatial total variation of the solution to increase. However, the increase in total variation is proved to be bounded in t>0 as a result of the uniform and exponential decay of the reactant to zero as t approaches infinity.