Existence of Solutions of the third term of the Connaughton-Newell Model with a source term

TL;DR

This paper proves the existence of solutions for the third operator in the Connaughton-Newell equation under specific assumptions, advancing understanding of this nonlinear kinetic model.

Contribution

It demonstrates the solvability of the third operator in the Connaughton-Newell equation with a constant kernel and well-behaved source term.

Findings

Proved the existence of solutions for the third operator.

Assumed a constant interaction kernel and well-behaved source.

Contributed to the mathematical understanding of the Connaughton-Newell model.

Abstract

The Connaughton-Newell equation is an approximation of three-wave kinetic equations using a fully non-linear coagulation-fragmentation model. This equation consists of three non-linear operators. In this paper, we proved that assuming a constant interaction kernel and a well-behaved source term, the third operator of the Connaughton-Newell equation has a solution.