  This paper is devoted to the well-posedness theory of piston problem for
compressible {combustion} Euler flows with physical ignition condition. A
significant combustion phenomena called detonation will occur provided the
reactant is compressed and ignited by a leading shock. Mathematically, the
problem can be formulated as an initial-boundary value problem for hyperbolic
balance laws with a large shock front as free boundary. In present paper, we
establish the global well-posedness of entropy solutions via wave front
tracking scheme within the framework of $BV\cap L^1$ space. The main
difficulties here stem from the discontinuous source term without uniform
dissipation structure, and from the characteristic-boundary associated with
degenerate characteristic field. In dealing with the obstacles caused by
ignition temperature, we develop a modified Glimm-type functional to control
the oscillation growth of combustion waves, even if the exothermic source fails
to uniformly decay. As to the characteristic boundary, the degeneracy of
contact discontinuity is fully employed to get elegant stability estimates near
the piston boundary. Meanwhile, we devise a weighted Lyapunov functional to
balance the nonlinear effects arising from large shock, characteristic boundary
and exothermic reaction, then obtain the $L^1-$stability of combustion wave
solutions. Our results reveal that one dimensional \emph{ZND} detonation waves
{supported} by a forward piston are indeed nonlinearly stable under small
perturbation in $BV$ sense. This is the first work on well-posedness of
inviscid reacting Euler fluids dominated by ignition temperature.
