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On a free boundary problem associated with combustion and solidification. (English) Zbl 0669.65089
The author considers two interface problems (flame propagation, solidification of a supercooled liquid) in which a dependence on the interface curvature appears. By simplifying both he establishes a common simpler problem for which a plane wave solution exists. The linear stability of the latter is investigated employing the Laplace transformation; by using a perturbation approach it is shown that an important feature of the solutions of the original interface problems, (the form of) the equation for the normal boundary velocity, has been retained in the simpler model problem. Finally, open questions are formulated.
Reviewer: G.Stoyan

MSC:
65Z05 Applications to the sciences
35R35 Free boundary problems for PDEs
35K05 Heat equation
80A25 Combustion
80A17 Thermodynamics of continua
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References:
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