Classical non mass preserving solutions of coagulation equations

TL;DR

This paper constructs classical solutions for coagulation equations with homogeneous kernels that demonstrate gelation, where mass is lost as particles become infinitely large in finite time.

Contribution

It introduces a method to construct classical solutions exhibiting gelation in coagulation equations with homogeneous kernels.

Findings

Demonstrates existence of solutions with gelation behavior.

Shows mass loss occurs in finite time due to infinite particle growth.

Provides mathematical framework for classical solutions in coagulation models.

Abstract

In this paper we construct classical solutions of a family of coagulation equations with homogeneous kernels that exhibit the behaviour known as gelation. This behaviour consists in the loss of mass due to the fact that some of the particles can become infinitely large in finite time.