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- W2950771668 abstract "The growth-fragmentation equation models systems of particles that grow and split as time proceeds. An important question concerns the large time asymptotic of its solutions. Doumic and Escobedo ($2016$) observed that when growth is a linear function of the mass and fragmentations are homogeneous, the so-called Malthusian behaviour fails. In this work we further analyse the critical case by considering a piecewise linear growth, namely begin{equation} c(x) = begin{cases} a_{_-} x quad quad x < 1 a_{_+} x quad quad x geq 1, end{cases} end{equation} with $0 < a_{_+} < a_{_-}$. We give necessary and sufficient conditions on the coefficients ensuring the Malthusian behaviour with exponential speed of convergence to an asymptotic profile, and also provide an explicit expression of the latter. Our approach relies crucially on properties of so-called refracted Levy processes that arise naturally in this setting." @default.
- W2950771668 created "2019-06-27" @default.
- W2950771668 creator A5028053340 @default.
- W2950771668 date "2018-12-19" @default.
- W2950771668 modified "2023-09-27" @default.
- W2950771668 title "On a family of critical growth-fragmentation semigroups and refracted L'evy processes" @default.
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