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Multi-dimensional travelling-wave solutions of a flame propagation model. (English) Zbl 0711.35066
The existence of a travelling wave solution \(u(x_ 1+ct,y)\) of the equation \[ \partial u/\partial t+\alpha (y)\partial u/\partial x_ 1=\Delta u+g(u)\text{ in } {\mathbb{R}}\times \omega \] is shown, where \(\omega\) is a bounded and smooth open domain. The function u satisfies an elliptic equation with parameter c where both u and c are unknown. In contrast to previous papers \(c+\alpha (y)\) may in general change the sign in the domain \(\omega\). Conditions for the occurrence of this phenomenon which may be interpreted as an inversion of the velocity field are given. The proofs are based on a priori estimates which are derived from methods typical for the elliptic case as the maximum principle, energy estimates, and elliptic regularity.
Reviewer: P.Kröger

35K57 Reaction-diffusion equations
80A25 Combustion
35J60 Nonlinear elliptic equations
Full Text: DOI
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