  In this paper we study the asymptotics of solutions to the Korteweg--de Vries
equation with steplike initial data, which lead to shock waves in the region
between the asymptotically constant region and the soliton region, as $t
\rightarrow \infty$. To achieve this, we present an alternative approach to the
usual argument involving a small norm Riemann--Hilbert problem, which is based
instead on the direct comparison of resolvents related to the corresponding
Riemann--Hilbert problems. The motivation for this approach stems from the fact
that an invertible holomorphic global parametrix solution for our problem does
not exist for certain discrete times.
