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

Abstract : 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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https://hal.archives-ouvertes.fr/hal-00683148
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Submitted on : Tuesday, February 19, 2013 - 4:48:03 PM
Last modification on : Monday, December 13, 2021 - 9:16:19 AM
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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 , AIMS, 2013, 6 (2), pp.219-243. ⟨10.3934/krm.2013.6.219⟩. ⟨hal-00683148v2⟩

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