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 journalArticleResearchpeer-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 languageEnglish
    Pages (from-to)219-243
    JournalKinetic and Related Models
    Volume6
    Issue number2
    DOIs
    Publication statusPublished - 1 Jun 2013

    Keywords

    • Eigenvalue problem
    • Entropy
    • Exponential convergence
    • Fragmentation
    • Growth
    • Long-time behavior

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