##
Global Entropy Solutions
to Exothermically Reacting, Compressible Euler Equations

#### Authors: Gui-Qiang Chen and David Wagner

#### Title:
Global Entropy Solutions
to Exothermically Reacting, Compressible Euler Equations

**Abstract**

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.

This article has appeared in:

*
Journal of Differential Equations
* **vol 191 **, Page 277-322, 2003.

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**Author Address**
Gui-Qiang Chen
Department of Mathematics
Northwestern University
Evanston, IL 60208-2730
gqchen@math.northwestern.edu