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

Pages: 775 - 790, Volume 3, Issue 4, December 2004

doi:10.3934/cpaa.2004.3.775       Abstract        Full Text (171.1K)       Related Articles

Dehua Wang - Department of Mathematics, University of Pittsburgh, Pittsburgh, PA 15260, United States (email)

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.

Keywords:  Combustion, reacting fluids, real flows, global solutions, existence, uniqueness, a-priori estimates.
Mathematics Subject Classification:  35B40, 35D05, 76V05, 35B45, 80A32.

Received: December 2003;      Revised: July 2004;      Published: September 2004.