Smoothness of moments of the solutions of discrete coagulation equations with diffusion

TL;DR

This paper proves the smoothness of moments in solutions to discrete coagulation-diffusion equations under certain growth and convergence conditions, ensuring global solutions without gelation.

Contribution

It establishes the smoothness of moments for solutions of coagulation-diffusion systems with sub-linear coagulation coefficients and positive diffusion limits, extending understanding of solution regularity.

Findings

Moments of solutions are smooth under specified conditions.

Global weak solutions exist without gelation.

Conditions include sub-linear growth and positive diffusion limits.

Abstract

In this paper, we establish smoothness of moments of the solutions of discrete coagulation-diffusion systems. As key assumptions, we suppose that the coagulation coefficients grow at most sub-linearly and that the diffusion coefficients converge towards a strictly positive limit (those conditions also imply the existence of global weak solutions and the absence of gelation).