Issue |
ESAIM: ProcS
Volume 62, 2018
CIMPA School on Mathematical Models in Biology and Medicine
|
|
---|---|---|
Page(s) | 30 - 42 | |
DOI | https://doi.org/10.1051/proc/201862030 | |
Published online | 17 October 2018 |
Explicit Solution and Fine Asymptotics for a Critical Growth-Fragmentation Equation
1
Sorbonne Universités, Inria, UPMC Univ Paris 06, Lab. J.L. Lions UMR CNRS 7598, Wolfgang Pauli Institute, University of Vienna, Paris, Vienna, France, Austria
2
Institute of Fundamental Sciences, Massey University, New Zealand
*
marie.doumic@inria.fr
**
B.vanBrunt@massey.ac.nz
We give here an explicit formula for the following critical case of the growth-fragmentation equation
for some constants g > 0, b > 0 and α >1 - the case α = 2 being the emblematic binary fission case. We discuss the links between this formula and the asymptotic ones previously obtained in [8], and use them to clarify how periodicity may appear asymptotically.
Résumé
Nous donnons ici une solution explicite de l’équation de croissance-fragmentation dans le cas critique suivant
pour des constantes g > 0, b > 0 et α > 1 - le cas α = 2 correspondant au cas emblématique de la fission binaire. Malgré l’absence de comportement auto-similaire ou stationnaire, nous employons cette formule pour mettre en évidence un comportement asymptotique périodique, de période variable en fonction de la courbe (t, x(t) = ert) suivie. Nous discutons également les liens entre cette formulation et celles obtenues précédemment dans [8].
© EDP Sciences, SMAI 2018
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