Weak Solutions to the Collision-Induced Breakage Equation with Dominating Coagulation

TL;DR

This paper establishes the existence and uniqueness of weak solutions to a collision-induced breakage and coagulation equation, especially when coagulation dominates for small volumes, extending previous results to more singular kernels.

Contribution

It introduces new existence and uniqueness results for weak solutions with more singular collision kernels and broader fragment distributions, under conditions of dominant coagulation.

Findings

Existence of weak solutions for more singular kernels.

Mass-conserving solutions for linearly growing kernels.

Broader class of fragment distribution functions included.

Abstract

Existence and uniqueness of weak solutions to the collision-induced breakage and coag-ulation equation are shown when coagulation is the dominant mechanism for small volumes. The collision kernel may feature a stronger singularity for small volumes than the ones considered in previous contributions. In addition, when the collision kernel is locally bounded, the class of fragment daughter distribution functions included in the analysis is broader. Mass-conserving solutions are also constructed when the collision kernel grows at most linearly at infinity and are proved to be unique for initial conditions decaying sufficiently fast at infinity. The existence proofs relies on a weak compactness approach in L 1 .