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Loss of mass in deterministic and random fragmentations. (English) Zbl 1075.60553
Summary: We consider a linear rate equation, depending on three parameters, that model fragmentation. For each of these fragmentation equations, there is a corresponding stochastic model, from which we construct an explicit solution to the equation. This solution is proved unique. We then use this solution to obtain criteria for the presence or absence of loss of mass in the fragmentation equation, as a function of the equation parameters. Next, we investigate small and large times asymptotic behavior of the total mass for a wide class of parameters. Finally, we study the loss of mass in the stochastic models.

MSC:
60J25 Continuous-time Markov processes on general state spaces
60J99 Markov processes
82C21 Dynamic continuum models (systems of particles, etc.) in time-dependent statistical mechanics
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