Global solution for the mixture of real compressible reacting flows in combustion
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.
Received: December 2003; Revised: July 2004; Published: September 2004.
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