ON THE ASYMPTOTIC BEHAVIOR OF HEATING TIMES
Chin-Huei Chang, Yun -shyong Chow, Zhen Wang · Analysis and Applications · 2003
An infinite homogeneous d-dimensional medium initially is at zero temperature, u=0. A heat impulse is applied at the origin, raising the temperature there to a value greater than a constant value u0>0. The temperature at the origin then decays, and when it reaches u0, another equal-sized heat impulse is applied at a normalized time τ1=1. Subsequent equal-sized heat impulses are applied at the origin at the normalized times τn, n=2,3,…, when the temperature there has decayed to u0. This sequence of normalized waiting times τn can be defined recursively by [Formula: see text] where d>0. This heat conduction problem was studied by Myshkis (J. Differential Equations Appl.3 (1997), 89–91), and he posed the problem to find an asymptotic expression for the τn as n→∞. The cases for dimensions d=1 and d≥3 have been treated by Chen, Chow, and Hsieh (J. Differential Equations Appl.6 (2000), 309–318). Here, we deal with the two-dimensional case, d=2.