On the existence or not of solutions to critical growth fragmentation equations

Date(s) : 19/09/2017   iCal
11 h 00 min - 12 h 00 min

A growth fragmentation equation with constant dislocation density measure will be considered, in which growth and division rates balance each other. This leads to a simple example of equation where the so called « Malthusian hypothesis » of
J. Bertoin and A. Watson (2016) is not necessarily satisfied. We will prove first, under suitable conditions, the existence and uniqueness of local non negative solutions satisfying natural boundedness conditions of its moments, and give their explicit analytical expression.
Then we will show that, when the « Malthusian hypothesis » is not satisfied, no global (or even local sometimes) non negative weak solution, satisfying some natural boundedness condition on its moments, exists. When a local non negative solution exists, the explicit expression is given.



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