On the Discrete Decay-Fragmentation Equation with Bounded Coagulation Rate


  • Luke Oluwaseye Joel* University of KwaZulu-Natal, Westville Campus, Durban
  • Jacek Banasiak University of Pretoria, Pretoria
  • Sergey Shindin University of KwaZulu-Natal, Westville Campus, Durban


The decay equation models an important real life phenomenon in which a substance can be removed from an aggregate of particles by chemical reaction, evaporation or dissolution. The decay process can be combined with the fragmentation and/or coagulation process. We examine the discrete decay-fragmentation equation with uniformly bounded coagulation rates. We prove the existence and uniqueness of physically meaningful solutions to this equation using the theory of semigroups of operators.


Arlotti, L. and Banasiak, J. (2004). Strictly substochastic semigroups with application to conservative and shattering solutions to fragmentation equations with mass loss, Journal of mathematical analysis and applications, 293(2):693 - 720

Banasiak, J. (2006). Shattering and non-uniqueness in fragmentation models - an analytic approach}. Physica D: Nonlinear Phenomena, 222(1):63 - 72.

Cai, M., Edwards, B. F., and Han, H. (1991). Exact and asymptotic scaling solutions for fragmentation with mass loss}, Physical Review A, 43(2):656-662.

Smith, A. L. (2011). Mathematical analysis of discrete coagulation-fragmentation equations}, PhD thesis, University of Strathclyde






Conference Contributions