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Article Dans Une Revue Communications in Mathematical Sciences Année : 2009

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

Résumé

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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Dates et versions

hal-00387408 , version 1 (25-05-2009)

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Philippe Laurençot, Benoît Perthame. Exponential decay for the growth-fragmentation/cell-division equation. Communications in Mathematical Sciences, 2009, 7 (2), p. 503-510. ⟨10.4310/CMS.2009.v7.n2.a12⟩. ⟨hal-00387408⟩
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