  In this paper, a novel observation is made on a one-dimensional compressible
Navier--Stokes model for the dynamic combustion of a reacting mixture of
$\gamma$-law gases ($\gamma>1$) with discontinuous Arrhenius reaction rate
function, on both bounded and unbounded domains. We show that the mass fraction
of the reactant (denoted as $Z$) satisfies a weighted gradient estimate $Z_y/
\sqrt{Z} \in L^\infty_t L^2_y$, provided that at time zero the density is
Lipschitz continuous and bounded strictly away from zero and infinity.
Consequently, the graph of $Z$ cannot form cusps or corners near the points
where the reactant in the combustion process is completely depleted at any
instant, and the entropy of $Z$ is bounded from above. The key ingredient of
the proof is a new estimate based on the Fisher information, first exploited by
[2, 7] with applications to PDEs in chemorepulsion and thermoelasticity. Along
the way, we also establish a Lipschitz estimate for the density.
