A mathematical model for collision-induced breakage is considered. Existence of weak solutions to the continuous nonlinear equation shown a large class unbounded collision kernels and daughter distribution functions, assuming kernel $K$ be given by $K(x,y)= x^{\alpha} y^{\beta} + x^{\beta} y^{\alpha}$ with $\alpha \le \beta 1$. When \in [1,2]$, it that there exists at least one mass-conserving ...