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Global solution for the mixture of real compressible reacting flows in combustion. (English) Zbl 1064.76091
Summary: 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.

##### MSC:
 76N10 Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics 35Q35 PDEs in connection with fluid mechanics 35B40 Asymptotic behavior of solutions to PDEs 35D05 Existence of generalized solutions of PDE (MSC2000) 76V05 Reaction effects in flows 35B45 A priori estimates in context of PDEs 80A32 Chemically reacting flows 76N15 Gas dynamics (general theory) 80A25 Combustion
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