The continuous coagulation and nonlinear multiple fragmentation equation

TL;DR

This paper establishes the existence, uniqueness, and mass conservation of solutions for a complex class of coagulation and fragmentation equations with singular kernels, advancing mathematical understanding of particle aggregation and breakup processes.

Contribution

It proves the existence and uniqueness of solutions for nonlinear coagulation and fragmentation equations with unbounded and singular kernels, including mass conservation.

Findings

Solutions exist globally and are unique.

Mass is conserved in the solutions.

Handles kernels with singularities and near-bilinear growth.

Abstract

The present paper deals with the existence and uniqueness of global classical solutions to the continuous coagulation and nonlinear multiple fragmentation equations for large classes of unbounded coagulation, collision and breakup kernels. In addition, it is shown that solutions are mass conserving. The coagulation and breakup kernels may have singularities on both the co-ordinate axes whereas the collision kernel grows up to bilinearity.