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The discrete collisional breakage equation, which captures the dynamics ofcluster growth when clusters encounter binary collisions with possible mattertransfer, is discussed in this article. The existence of global mass-conservingsolutions is investigated for the collision kernels $a_{i,j}=A(i^{\alpha}j^{\beta} + i^{\beta}j^{\alpha})$, $i, j \ge 1$, with $\alpha \in (-\infty,1)$,$\beta\in [\alpha,1]\cap (0,1]$, and $A>0$ and for a large class of possiblyunbounded daughter distribution functions. All algebraic superlinear moments ofthese solutions are bounded on time intervals $[T,\infty)$ for any $T>0$. Theuniqueness issue is further handled under additional restrictions on theinitial data. Finally, non-trivial stationary solutions are constructed by adynamical approach.

The discrete collision-induced breakage equation with mass transfer: well-posedness and stationary solutions