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

Abstract

The discrete collisional breakage equation, which captures the dynamics of cluster growth when clusters encounter binary collisions with possible matter transfer, is discussed in this article. The existence of global mass-conserving solutions 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 possibly unbounded daughter distribution functions. All algebraic superlinear moments of these solutions are bounded on time intervals $[T,\infty)$ for any $T>0$. The uniqueness issue is further handled under additional restrictions on the initial data. Finally, non-trivial stationary solutions are constructed by a dynamical approach.