Publication: On a Family of Critical Growth-Fragmentation Semigroups and Refracted Lévy Processes
On a Family of Critical Growth-Fragmentation Semigroups and Refracted Lévy Processes
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Cavalli, B. (2020). On a Family of Critical Growth-Fragmentation Semigroups and Refracted Lévy Processes. Acta Applicandae Mathematicae, 166(1), 161–186. https://doi.org/10.1007/s10440-019-00261-5
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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 (Kinet. Relat. Models, 9(2):251–297, [12]) 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 c(x)={a−xx<1a+xx≥1, with 0
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- Cavalli, Benedetta
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Cavalli, B. (2020). On a Family of Critical Growth-Fragmentation Semigroups and Refracted Lévy Processes. Acta Applicandae Mathematicae, 166(1), 161–186. https://doi.org/10.1007/s10440-019-00261-5