Investigation of the kinetic equation of cascade fragmentation theory at not self-similar subdivision

Abstract

The cascade kinetic fragmentation process of solids is investigated when the condition probability density of splinter formation do not depends on time and has the property $P(\rho, r, t) = P(\rho/r)$. It is obtained the evolution equation for the probability distribution density in terms of its Mellin transformation. In the particular case $P(\rho/r) = C (\rho/r)^\alpha$, the limit solution of this equation at $t \to \infty$ is found. It differs essentially from the Kolmogorov law.