The study of collision‐induced breakage phenomenon in the particulate process has much current interest. This is an important process arising in many engineering disciplines. In this work, the existence of continuous solution of the pure collisional breakage model is developed beneath some restrictions on the breakage kernels. Furthermore, the mass conservation and uniqueness of solution are investigated in the absence of “shattering transition.” The underlying theory is based on the compactness result of Arzelà‐Ascoli and Banach contraction mapping principle.

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Modelling and simulation of collisional particle breakage mechanisms are crucial in several physical phenomena (asteroid belts, molecular clouds, raindrop distribution etc.) and process industries (chemical, pharmaceutical, material etc.). This paper deals with the development and analysis of schemes to numerically solve the multi-dimensional nonlinear collisional fragmentation model. Two numerical techniques are presented based on the finite volume discretization method. It is shown that the proposed schemes are consistent with the hypervolume conservation property. Moreover, the number preservation property law also holds for one of them. Detailed mathematical discussions are presented to establish the convergence analysis and consistency of the multi-dimensional schemes under predefined restrictions on the kernel and initial data. The proposed schemes are shown to be second-order convergent. Finally, several numerical computations (one-, two- and three-dimensional fragmentation) are performed to validate the numerical schemes.

This article is devoted to the study of existence of a mass conserving global solution for the collision-induced nonlinear fragmentation model which arises in particulate processes, with the following type of collision kernel: \[C(x,y)~\le~k_1 \frac{(1 + x)^\nu (1 + y)^\nu}{\left(xy\right)^\sigma},\] for all ~$x, y \in (0,\infty)$, where $k_1$ is a positive constant, $\sigma \in \left[0,\tfrac{1}{2}\right]$ and $\nu \in [0, 1]$. The above-mentioned form includes many practical oriented kernels of both \emph{singular} and \emph{non-singular} types. The singularity of the unbounded collision kernel at coordinate axes extends the previous existence result of Paul and Kumar [Mathematical Methods in the Applied Sciences 41 (7) (2018) 2715–2732 (\href{https://doi.org/10.1002/mma.4775}{doi:10.1002/mma.4775})] and also exhibits at most quadratic growth at infinity. Finally, uniqueness of solution is also investigated for pure singular collision rate, i.e., for ~ $\nu=0$.

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