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Nonadiabatic plane laminar flames and their singular limits. (English) Zbl 0714.34042

New results concerning nonadiabatic travelling waves and their singular limits are presented. By means of standard combustion approximations the model reduces to a two-point boundary value problem on the real line with an eigenvalue:

-u '' +cu ' =f(u)v n -λg(u),-v '' +cv ' =-f(u)v n ,u(-)=0,v(-)=1,u(+)=0,v ' (+)=0·

Here u denotes the reduced temperature, v the reactant mass fraction, c the reduced mass flux, f the reduced source term, λ the reduced heat loss rate in the hot gases, and g the reduced heat loss rate function.

The natural problem would be to find a nontrivial solution (u,v,c), with (u,v)(0,1) and c>0. Existence of a solution is achieved by first considering the problem in a bounded domain and then by taking an infinite domain limit. The author proves strong convergence of the nonadiabatic travelling wave to singular limit free-boundary solutions with discontinuous derivatives.

Reviewer: L.M.Berkovich
34B15Nonlinear boundary value problems for ODE
34E20Asymptotic singular perturbations, turning point theory, WKB methods (ODE)
34L05General spectral theory for OD operators
80A25Combustion, interior ballistics
34B10Nonlocal and multipoint boundary value problems for ODE