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

Daniel Balagué; José A. Cañizo; Pierre Gabriel

doi:10.3934/krm.2013.6.219

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

Daniel Balagué, José A. Cañizo, Pierre Gabriel

Research output: Contribution to journal › Article › Research › peer-review

19 Citations (Scopus)

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 +∞. 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. © American Institute of Mathematical Sciences.

Original language	English
Pages (from-to)	219-243
Journal	Kinetic and Related Models
Volume	6
Issue number	2
DOIs	https://doi.org/10.3934/krm.2013.6.219
Publication status	Published - 1 Jun 2013

Keywords

Eigenvalue problem
Entropy
Exponential convergence
Fragmentation
Growth
Long-time behavior

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title = "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 +∞. 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. {\textcopyright} American Institute of Mathematical Sciences.",

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N2 - 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 +∞. 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. © American Institute of Mathematical Sciences.

AB - 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 +∞. 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. © American Institute of Mathematical Sciences.

KW - Eigenvalue problem

KW - Entropy

KW - Exponential convergence

KW - Fragmentation

KW - Growth

KW - Long-time behavior

U2 - 10.3934/krm.2013.6.219

DO - 10.3934/krm.2013.6.219

M3 - Article

VL - 6

SP - 219

EP - 243

JO - Kinetic and Related Models

JF - Kinetic and Related Models

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