Global existence and asymptotic analysis of solutions to a model for the dynamic combustion of compressible fluids

Konstantina Trivisa

doi:10.3934/proc.2003.2003.852

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2003, Volume 2003: 852-863. Doi: 10.3934/proc.2003.2003.852 open access

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Global existence and asymptotic analysis of solutions to a model for the dynamic combustion of compressible fluids

Konstantina Trivisa^1,

1.
Department of Mathematics, University of Maryland, College Park, MD 20742

Received: September 2002

Revised: April 2003

Published: April 2003

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Abstract

A model is introduced for the dynamic combustion of exothermically reacting, compressible fluids formulated by the Navier-Stokes equations expressing the conservation of mass, the balance of momentum and energy and the two species chemical kinetics. The global existence of the discontinuous solutions to the Navier- Stokes equations with large discontinuous initial data is established by combining the difference approximations techniques and energy estimates. The asymptotic analysis of solutions is also discussed.

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Mathematics Subject Classification: 35B40, 35D05, 76N10, 35B45.

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