# American Institute of Mathematical Sciences

August  2005, 5(3): 529-542. doi: 10.3934/dcdsb.2005.5.529

## Universality of dishonesty of substochastic semigroups: Shattering fragmentation and explosive birth-and-death processes

 1 School of Mathematical Sciences, University of KwaZulu-Natal, Durban 4041 2 Laboratoire de Mathématiques, Université de Franche-Comté, Route de Gray, 25030 Besançon Cedex, France

Received  April 2004 Revised  June 2004 Published  May 2005

By a dishonest process we understand a process in which, for some initial data, there occurs an unaccounted for loss of the described quan- tity throughout the evolution. Classical examples are offered by shattering fragmentation, where the total mass is decreasing faster than predicted by the formal conservation laws, or explosive birth-and-death processes which, being formally conservative, suffer from the loss of individuals in the course of evo- lution. In this note we shall show, for these two processes, that if dishonesty occurs for one initial datum, then it must occur for any of them.
Citation: Jacek Banasiak, Mustapha Mokhtar-Kharroubi. Universality of dishonesty of substochastic semigroups: Shattering fragmentation and explosive birth-and-death processes. Discrete & Continuous Dynamical Systems - B, 2005, 5 (3) : 529-542. doi: 10.3934/dcdsb.2005.5.529
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