Aggregation With Catalytically Activated Fragmentation: Existence, Nonexistence, and Asymptotic Analysis of Solutions

ABSTRACT We study the mathematical model of aggregation with catalytically activated fragmentation, governed by a nonlinear fragmentation equation. This aggregation‐fragmentation framework, in which collisions trigger fragmentation events, is a key tool for analyzing systems with high dispersed‐phase loading. In this article, we prove the global existence of mass‐conserving strong solutions for classes of aggregation kernels satisfying the growth condition . We also address the uniqueness and long‐time behavior of the solution. Furthermore, this study is extended to analyze the case where no mass‐conserving solution exists over any finite time interval when the aggregation kernel satisfies , where . Finally, we perform several numerical experiments to demonstrate strong agreement with the rigorously established theoretical results concerning the behavior of the solution.