Abstract :
A mathematical model for viscous, real, compressible, reactive fluid flows is considered.
The existence of global solutions for the free boundary problem with species diffusion
in dynamic combustion is established when the viscosity λ depends on the density
i.e., λ(ρ) = Aρα (0 < α 12
), where A is a generic positive constant. Furthermore, the
equations of state depend nonlinearly on density and temperature unlike the case of
perfect gases or radiative flows. In addition, the shock wave, turbulence, vacuum, mass
concentration or extremely hot spot will not be developed in any finite time if the initial
data do not contain vacuum.
