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We consider solutions to a free boundary problem for the heat equation, describing the propagation of flames. Suppose there is a bounded domain Ω ⊂ QT = Rn x (0,T) for some T > 0 and a function u > 0 in Ω such that
ut = Δu, in Ω,
u = 0 and |∇u| = 1, on Γ := ∂Ω ∩ QT,
u(·,0) = u0, on Ω0,
...
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