Mass conserving global solutions for the nonlinear collision-induced fragmentation model with a singular kernel

TL;DR

This paper proves the existence and uniqueness of mass-conserving global solutions for a nonlinear fragmentation model with a singular collision kernel, extending previous results to more practical kernels with singularities.

Contribution

It introduces new existence and uniqueness results for a nonlinear fragmentation model with a singular collision kernel, including unbounded and quadratic growth cases.

Findings

Existence of mass-conserving global solutions established.

Solutions are unique under specified conditions.

Model includes practical kernels with singularities.

Abstract

This article is devoted to the study of existence of a mass conserving global solution for the collision-induced nonlinear fragmentation model which arises in particulate processes, with the singular type of collision kernel. The above mentioned form includes many practical oriented kernels of both singular and non-singular types. The singularity of the unbounded collision kernel at coordinate axes extends the previous existence result and also exhibits at most quadratic growth at infinity. Finally, uniqueness of solution is also investigated.