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Global solution for the mixture of real compressible reacting flows in combustion

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  • 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.
    Mathematics Subject Classification: 35B40, 35D05, 76V05, 35B45, 80A32.

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