# American Institute of Mathematical Sciences

2003, 2003(Special): 888-897. doi: 10.3934/proc.2003.2003.888

## Global existence and dynamical properties of large solutions for combustion flows

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

Received  July 2002 Published  April 2003

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.
Citation: Dehua Wang. Global existence and dynamical properties of large solutions for combustion flows. Conference Publications, 2003, 2003 (Special) : 888-897. doi: 10.3934/proc.2003.2003.888
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