Existence and stability of a planar wave solution to a combustion model

Thesis/Dissertation · Wed Jan 01 04:00:00 EST 1992

OSTI ID:7019238

Lang, C L

The authors consider a model for a premixed flame arising from a single step chemical reaction with one reactant involved. This model gives a system of reaction-diffusion equations. Planar wave solutions of this system satisfy a system of O.D.E.'s with specified boundary conditions. The authors want to study the existence and stability of a planar wave solution of the system. To study the existence problem, they use a shooting argument in four dimensional phase space of the O.D.E.'s. This gives the existence of a planar wave solution for Lewis number equals one or 1 + [epsilon]l. For the stability of a planar wave solution, they consider a one dimensional perturbation to the planar wave solution. In this situation, the stability problem is equivalent to the linearly stability problem if one were in a properly weighted space. The linearly stability problem is governed by the function D([sigma], k, l). The authors derived the explicit formula of this function and discuss some stability problems of a planar wave solution in this paper.

• Research Organization: Ohio State Univ., Columbus, OH (United States)
• OSTI ID: 7019238
• Country of Publication: United States
• Language: English

Related Subjects

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CHEMISTRY
400800* -- Combustion
Pyrolysis
& High-Temperature Chemistry
99 GENERAL AND MISCELLANEOUS
990200 -- Mathematics & Computers
ANALYTICAL SOLUTION
CHEMICAL REACTIONS
COMBUSTION
EQUATIONS
MATHEMATICAL MODELS
OXIDATION
PREDICTION EQUATIONS
THERMOCHEMICAL PROCESSES