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 U0 and 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.
Tarzia, D. A. (1990). A variant of the heat balance integral method and a new proof of the exponentially fast asymptotic behavior of the solutions in heat conduction problems with absorption. International Journal of Engineering Science, 28(12), 1253–1259. https://doi.org/10.1016/0020-7225(90)90073-R