Open Access
June 2009 Exponential decay for the growth-fragmentation/cell-division equations
Philippe Laurençot, Benoit Perthame
Commun. Math. Sci. 7(2): 503-510 (June 2009).


We consider the linear growth-fragmentation equation arising in the modelling of cell division or polymerisation processes. For constant coefficients, we prove that the dynamics converges to the steady state with an exponential rate. The control on the initial data uses an elaborate $L1$-norm that seems to be necessary. It also reflects the main idea of the proof, which is to use an anti-derivative of the solution. The main technical difficulty is related to the entropy dissipation rate, which is too weak to produce a Poincaré inequality.


Download Citation

Philippe Laurençot. Benoit Perthame. "Exponential decay for the growth-fragmentation/cell-division equations." Commun. Math. Sci. 7 (2) 503 - 510, June 2009.


Published: June 2009
First available in Project Euclid: 27 May 2009

zbMATH: 1183.35038
MathSciNet: MR2536450

Primary: 35B40 , 45K05 , 82D60 , 92D25

Keywords: Cell division , Convergence to equilibrium , Growth-fragmentation equations , polymerisation process , size repartition , temporal rate of convergence

Rights: Copyright © 2009 International Press of Boston

Vol.7 • No. 2 • June 2009
Back to Top