Table of Contents
ISRN Mathematical Analysis
Volume 2013 (2013), Article ID 908753, 7 pages
http://dx.doi.org/10.1155/2013/908753
Research Article

On the Honesty in Nonlocal and Discrete Fragmentation Dynamics in Size and Random Position

Department of Mathematical Sciences, North-West University, Mafikeng 2735, South Africa

Received 19 April 2013; Accepted 22 May 2013

Academic Editors: M. Escobedo and K. Ezzinbi

Copyright © 2013 S. C. Oukouomi Noutchie and E. F. Doungmo Goufo. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

A discrete initial-value problem describing multiple fragmentation processes, where the fragmentation rate is size and position dependent and where new particles are spatially randomly distributed according to some probabilistic law, is investigated by means of parameter-dependent operators together with the theory of substochastic semigroups with a parameter. The existence of semigroups is established for each parameter and “glued” together so as to obtain a semigroup to the full space. Under certain conditions on each fragmentation rate, we used Kato’s Theorem in to show the existence of the generator and we provide sufficient conditions for honesty.