  Interstellar dust (ISD) penetrates into the heliosphere due to the relative
motion of the Sun and the local interstellar medium (LISM). Inside the
heliosphere and at the boundaries, where solar wind interacts with the LISM,
distribution of ISD is modified due to the action of the electromagnetic
forces, the solar gravitation and the radiation pressure. These forces make the
distribution of the ISD particles in the heliosphere inhomogeneous. In previous
work we demonstrated the existence of singularities in the ISD density
distribution at 0.03 - 10 a.u. north and south with respect to the heliospheric
current sheet. In this paper we show that dispersion in the ISD velocity
distribution strongly affects the singularities. Even small values of
dispersion have the drastic impact on the density distribution and smooth the
high density layers discovered previously.
