10th session, April 13th 2015
Monday 13th EHESS, 190-198 Avenue de France, room 466, 4th floor - 75013 Paris
14h : Marie Doumic (INRIA)
A limit case for the fragmentation and growth-fragmentation equation (in collaboration with M. Escobedo)
The long-time asymptotics of the fragmentation and growth-fragmentation equations have been studied by many authors, proving convergence toward a steady behaviour under balance assumptions on the coefficients. Exponential speed of convergence has also been established under more restrictive assumptions.
We focus here on a limit case where no such behaviour is possible, since the usual balance assumptions are not satisfied. We show that a specific dynamics emerge, where the initial condition continues to play a major role in the asymptotic profile. We also link our results with probabilistic results obtained by J. Bertoin and B. Haas.
The long-time asymptotics of the fragmentation and growth-fragmentation equations have been studied by many authors, proving convergence toward a steady behaviour under balance assumptions on the coefficients. Exponential speed of convergence has also been established under more restrictive assumptions.
We focus here on a limit case where no such behaviour is possible, since the usual balance assumptions are not satisfied. We show that a specific dynamics emerge, where the initial condition continues to play a major role in the asymptotic profile. We also link our results with probabilistic results obtained by J. Bertoin and B. Haas.