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Article Dans Une Revue Kinetic and Related Models Année : 2013

Fine asymptotics of profiles and relaxation to equilibrium for growth-fragmentation equations with variable drift rates

Daniel Balagué
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José Cañizo
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Pierre Gabriel

Résumé

We are concerned with the long-time behavior of the growth-fragmentation equation. We prove fine estimates on the principal eigenfunctions of the growth-fragmentation operator, giving their first-order behavior close to $0$ and $+\infty$. Using these estimates we prove a spectral gap result by following the technique in [Caceres, Canizo, Mischler 2011, JMPA], which implies that solutions decay to the equilibrium exponentially fast. The growth and fragmentation coefficients we consider are quite general, essentially only assumed to behave asymptotically like power laws.
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Dates et versions

hal-00683148 , version 1 (27-03-2012)
hal-00683148 , version 2 (19-02-2013)

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Daniel Balagué, José Cañizo, Pierre Gabriel. Fine asymptotics of profiles and relaxation to equilibrium for growth-fragmentation equations with variable drift rates. Kinetic and Related Models , 2013, 6 (2), pp.219-243. ⟨10.3934/krm.2013.6.219⟩. ⟨hal-00683148v2⟩
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