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Global solution for the mixture of real compressible reacting flows in combustion
The equations for viscous, compressible, heat-conductive, real
reactive flows in dynamic combustion are considered, where the
equations of state are nonlinear in temperature unlike the linear
dependence for perfect gases. The initial-boundary value problem
with Dirichlet-Neumann mixed boundaries in a finite domain is
studied. The existence, uniqueness, and regularity of global
solutions are established with general large initial data in
$H^1$. It is proved that, although the solutions have large
oscillations, there is no shock wave, turbulence, vacuum, mass
concentration, or extremely hot spot developed in any finite time.