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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: \[ -u''+cu'=f(u)v^ n-\lambda g(u),\quad -v''+cv'=- f(u)v^ n,\quad u(-\infty)=0,\quad v(-\infty)=1,\quad u(+\infty)=0,\quad v'(+\infty)=0. \] Here u denotes the reduced temperature, v the reactant mass fraction, c the reduced mass flux, f the reduced source term, \(\lambda\) 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)\(\neq (0,1)\) 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

MSC:

34B15 Nonlinear boundary value problems for ordinary differential equations
34E20 Singular perturbations, turning point theory, WKB methods for ordinary differential equations
34L05 General spectral theory of ordinary differential operators
80A25 Combustion
34B10 Nonlocal and multipoint boundary value problems for ordinary differential equations
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