  We consider unsteady ballistic heat transport in a semi-infinite Hooke chain
with free end and arbitrary initial temperature profile. An analytical
description of the evolution of the kinetic temperature is proposed in both
discrete (exact) and continuum (approximate) formulations. By comparison of the
discrete and continuum descriptions of kinetic temperature field, we reveal
some restrictions to the latter. Specifically, the far-field kinetic
temperature is well described by the continuum solution, which, however,
deviates near and at the free end (boundary). We show analytically that, after
thermal wave reflects from the boundary, the discrete solution for the kinetic
temperature undergoes a jump near the free end. A comparison of the
descriptions of heat propagation in the semi-infinite and infinite Hooke chains
is presented. Results of the current paper are expected to provide insight into
non-stationary heat transport in the semi-infinite lattices.
