This report is limited to calling attention to a feature of the ideal interplanetary blastwave according to the Parker type of formal theory which has not been scrutinized in the literature before. It is shown analytically that, on account of inertial effects, a gradient singularity of the radial momentum transfer rate arises in association with the local coronal accumulation in front of the rear propelling contact surface postulated in the theory and that such a local accumulation is a general result for power-law explosive waves extruding against an ambient hydrogen solar wind having a strictly inverse-square radial decay in density. The usual numerical schemes are rendered ineffective for the determination of the expected singular local-wave behavior. To circumvent the difficulty, a combined numerical-integral technique has been developed and in this work it has been applied on six specific model waves, including both the decelerating and the non-decelerating, which have energies increasing with time as t K with K = 28, 4, 1, 1/2, 1/4 and 1/8, respectively. Also, a local solution corresponding to the limiting approximation of a constant material velocity gradient has been analytically constructed. The importance of the local singular behavior is quantitatively appraised and certain interplanetary implications are given cursory inferences. It is considered that the new results should have inescapable relevance with regard to (1) the quantitative determination of the progressive peak transverse magnetic field during an interplanetary storm and (2) the theoretical determination of the macroscopic stability of the postulated contact surface.