  On the basis of local nonequilibrium approach, the one-dimensional model of
the solute diffusion during rapid solidification of the binary alloy in the
semi-infinite volume is considered. Within the scope of the model it is
supposed that mass transport is described by the telegrapher equation. The
basic assumption concerns the behavior of the diffusion flux and the solute
concentration at the interface. Under the condition that these quantities are
given by the superposition of the exponential functions the solutions of the
telegrapher equation determining the flux and the solute distributions in the
melt have been found. On the basis of these solutions different regimes of the
solidification in the near surface region and the behavior of the partition
coefficient have been investigated. The concentration profiles in the solid
after complete solidification are analyzed depending on the model parameters.
