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arXiv · 1203.6156

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

Daniel Balagué·José Cañizo·Pierre Gabriel
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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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Daniel Balagué, José Cañizo, Pierre Gabriel. 2012-03-28. Fine asymptotics of profiles and relaxation to equilibrium for growth-fragmentation equations with variable drift rates. https://doi.org/10.3934/krm.2013.6.219

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