Exponential decay for the growth-fragmentation/cell-division equation

2009/01/30 by Philippe Laurençot, Benoı̂t Perthame, Laurençot, Philippe +1 · 1 citation
Mathematics · #35B40 #45K05 #82D60 #92D25 #Analysis of PDEs (math.AP) #FOS: Mathematics #Mathematical Biology Tumor Growth #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.0901.4880

openalex publication_date 2009/01/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/30

Abstract

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.

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