The behavior of the blast impulse initiated by a point blast in the dusty air is investigated theoretically. It is shown that the jumps of parameters at the shock front in the dusty air follow other regularities in comparison with the case of an ideal gas, beginning from the distance of three dynamic radii, so at ten dynamic radii the difference in overpressure exceeds 60%. When the air heterogeneity is taken into account, substantial gradual changes of wave profile come over and the total blast wave impulse can't be determined by the front overpressure only. The known far asymptotic law takes no place in the point blast flow at the volume dust densities rho(20) > 3.10(-3) kg/m(3). In contrast to the ideal gas, the shock front discontinuity vanishes in the dusty air at a finite distance from its origin and the blast wave eventually turns into a dispersive wave without discontinuity. The wave structure changing is studied in the process of the shock wave transformation into the dispersive wave. (C) 2013 Elsevier Ltd. All rights reserved.