Explicit Solution and Fine Asymptotics for a Critical Growth-Fragmentation Equation

Abstract : We give here an explicit formula for the following critical case of the growth-fragmentation equation $$\frac{\partial}{\partial t} u(t, x) + \frac{\partial}{\partial x} (gxu(t, x)) + bu(t, x) = b\alpha^2 u(t, \alpha x), \qquad u(0, x) = u_0 (x),$$ for some constants $g > 0$, $b > 0$ and $\alpha > 1$ - the case $\alpha = 2$ being the emblematic binary fission case. We discuss the links between this formula and the asymptotic ones previously obtained in (Doumic, Escobedo, Kin. Rel. Mod., 2016), and use them to clarify how periodicity may appear asymptotically.
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https://hal.archives-ouvertes.fr/hal-01510960
Contributor : Marie Doumic <>
Submitted on : Monday, November 19, 2018 - 9:25:49 AM
Last modification on : Wednesday, May 15, 2019 - 4:02:50 AM
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Marie Doumic, Bruce van Brunt. Explicit Solution and Fine Asymptotics for a Critical Growth-Fragmentation Equation. ESAIM: Proceedings and Surveys, 62, pp.30-42, 2018, ⟨10.1051/proc/201862030⟩. ⟨hal-01510960v2⟩

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