Asymptotic behavior of solutions to the coagulation-fragmentation equations. II. Weak fragmentation

Asymptotic Behaviour of Solutions to the Coagulation - Fragmentation Equations

Weak solutions to the continuous coagulation equation with multiple fragmentation

The existence of weak solutions to the continuous coagulation equation with multiple fragmentation is shown for a class of unbounded coagulation and fragmentation kernels, the fragmentation kernel having possibly a singularity at the origin. This result extends previous ones where either boundedness of the coagulation kernel or no singularity at the origin for the fragmentation kernel was assumed.

Existence and Uniqueness of Density Conserving Solutions to the Coagulation-Fragmentation Equations With Strong Fragmentation

Asymptotic Analysis of Coagulation–Fragmentation Equations of Carbon Nanotube Clusters

The possibility of the existence of single-wall carbon nanotubes (SWNTs) in organic solvents in the form of clusters is discussed. A theory is developed based on a bundlet model for clusters describing the distribution function of clusters by size. The phenomena have a unified explanation in the framework of the bundlet model of a cluster, in accordance with which the free energy of an SWNT inv...

Global strict solutions to continuous coagulation-fragmentation equations with strong fragmentation

In this paper we give an elementary proof of the unique, global-in-time solvability of the coagulation-(multiple) fragmentation equation with polynomially bounded fragmentation and particle production rates and a bounded coagulation rate. The proof relies on a new result concerning domain invariance for the fragmentation semigroup which is based on a simple monotonicity argument.