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

2 MAMBA - Modelling and Analysis for Medical and Biological Applications
Inria de Paris, LJLL - Laboratoire Jacques-Louis Lions
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.
Keywords :
Document type :
Directions of work or proceedings

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
Long-term archiving on : Wednesday, February 20, 2019 - 12:33:53 PM

### Files

BruceMarie_Proc_def_hal.pdf
Files produced by the author(s)

### Citation

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⟩

Record views