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

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  • We are concerned with the long-time behavior of the growth-frag-mentation 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 [1], 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.
    Mathematics Subject Classification: Primary: 35B40, 45C05, 45K05; Secondary: 82D60, 92C37.


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