  The paper deals with a problem of asymptotic step-like solutions to the
Burgers' equation with variable coefficients and a small parameter. By means of
the non-linear WKB method, the algorithm of constructing these asymptotic
solutions is proposed and statements on justification of the algorithm are
proved.
  The obtained results are illustrated by an example, for which the first
asymptotic step-like approximation is explicitly found. The asymptotic solution
is global, and has a form of the shock wave type function. There are also given
graphs of these approximate solutions for certain numerical parameters.
