# American Institute of Mathematical Sciences

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