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Global existence and dynamical properties of large solutions for combustion flows

Pages: 888 - 897, Issue Special, July 2003

 Abstract        Full Text (184.9K)              

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

Abstract: A mathematical model for viscous compressible realistic reactive flows without species diffusion in dynamic combustion is investigated. 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 and the chemical reaction generates heat, there is no shock wave, turbulence, vacuum, mass or heat concentration developed in a finite time.

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

Received: July 2002; Published: April 2003.