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A discrete version of the nonlinear collision-induced breakage equation isstudied. Existence of solutions is investigated for a broad class of unboundedcollision kernels and daughter distribution functions, the collision kernel$a_{i,j}$ satisfiying $a_{i,j} \leq A i j$ for some $A>0$. More precisely, itis proved that given suitable conditions, there exists at least onemass-conserving solution for all times. A result on the uniqueness of solutionsis also demonstrated under reasonably general conditions. Furthermore, thepropagation of moments, differentiability, and the continuous dependence ofsolutions are established, along with some invariance properties and thelarge-time behaviour of solutions.

Well-posedness to the discrete collision-induced breakage equation and various properties of solutions