We give a new and explicit estimate for the asymptotic behavior of the solutions of the problem ut- uxx+ u+P= 0, x > 0,t> 0, with conditions u(0, t) = 1, t > 0 and u(x, 0) = U0(x) ≥ 0, x > 0, for a class of functions U0and parameter 0 < p < 1. We use an approximate solution given by the heat balance integral method with the innovation property which fixes appropriately the asymptotic limit of the corresponding approximate free boundary. © 1990.
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