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A heat conduction problem with the temperature measured away from the heating point

An infinite homogeneous -dimensional medium initially is at zero temperature. A heat impulse is applied at the origin, raising the temperature at the observation point to a value greater than a constant value . The temperature there then decays and when it reaches at time , another equal-sized heat impulse is applied at the origin. Subsequent equal-sized heat impulses are applied at the origin at times , when the temperature at the observation point has decayed to . This sequence of heating times can be defined recursively by a difference equation and its asymptotic behaviour is studied in this paper. A similar heat conduction problem in which the observation point is set at the origin was first studied by Myshkis in Journal of Difference Equations and Applications 3 (1997), 89–91.