December  2004, 3(4): 775-790. doi: 10.3934/cpaa.2004.3.775

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

1. 

Department of Mathematics, University of Pittsburgh, Pittsburgh, PA 15260, United States

Received  December 2003 Revised  July 2004 Published  September 2004

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.
Citation: Dehua Wang. Global solution for the mixture of real compressible reacting flows in combustion. Communications on Pure & Applied Analysis, 2004, 3 (4) : 775-790. doi: 10.3934/cpaa.2004.3.775
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