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Stability of travelling fronts in a model for flame propagation. I: Linear analysis. (English) Zbl 0763.76033
Im Zusammenhang mit der Berechnung der Flammenausbreitung muß ein Gleichungssystem der Form \(u_ t-\Delta u+\alpha (y)u_ x=vf(u)\), \(v_ t-(\Delta v/Le)+\alpha (y)v_ x=-vf(u)\) gelöst werden. Dabei ist \(Le\) die Lewis-Zahl, die hier gleich eins gesetzt wird. Unter bestimmten Annahmen über die Funktion \(f(u)\) hat das System Lösungen in Form von laufenden Wellen (travelling wave solutions): \(u(t,x,y)=\phi(x+ct,y)\); \(v(t,x,y)=\psi(x+ct,y)\). Es wird gezeigt, daß derartige Lösungen gegenüber kleinen Störungen stabil sind. Dazu wird das obige Gleichungssystem um eine travelling wave solution linearisiert, und es werden die Eigenwerte der so entstandenen Gleichungen untersucht.
Reviewer: M.Heckl (Berlin)

MSC:
76E99 Hydrodynamic stability
76V05 Reaction effects in flows
80A25 Combustion
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