Well-posedness of the coagulation-fragmentation equation with size diffusion

TL;DR

This paper investigates the well-posedness of the coagulation-fragmentation equation with size diffusion, utilizing a semigroup approach based on linear operator generation results in weighted spaces.

Contribution

It establishes local and global well-posedness for the equation by leveraging semigroup theory and previous linear operator results.

Findings

Proved local well-posedness of the equation.

Established conditions for global solutions.

Extended the analysis to weighted L^1 spaces.

Abstract

Local and global well-posedness of the coagulation-fragmentation equation with size diffusion are investigated. Owing to the semilinear structure of the equation, a semigroup approach is used, building upon generation results previously derived for the linear fragmentation-diffusion operator in suitable weighted $L^1$-spaces.