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

Dehua Wang

doi:10.3934/cpaa.2004.3.775

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2004, Volume 3, Issue 4: 775-790. Doi: 10.3934/cpaa.2004.3.775

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

Dehua Wang^1,

1.
Department of Mathematics, University of Pittsburgh, Pittsburgh, PA 15260

Received: November 30, 2003

Revised: June 30, 2004

Published: November 2004

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Abstract

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.

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

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