Spectral gap for the growth-fragmentation equation via harris's theorem

Jose A. Canizo*, Pierre Gabriel, Havva Yoldas

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

3 Citations (Scopus)


We study the long-time behavior of the growth-fragmentation equation, a nonlocal linear evolution equation describing a wide range of phenomena in structured population dynamics. We show the existence of a spectral gap under conditions that generalize those in the literature by using a method based on Harris's theorem, a result coming from the study of equilibration of Markov processes. The difficulty posed by the nonconservativeness of the equation is overcome by performing an h-transform, after solving the dual Perron eigenvalue problem. The existence of the direct Perron eigenvector is then a consequence of our methods, which prove exponential contraction of the evolution equation. Moreover the rate of convergence is explicitly quantifiable in terms of the dual eigenfunction and the coefficients of the equation.

Original languageEnglish
Pages (from-to)5185-5214
Number of pages30
JournalSIAM Journal on Mathematical Analysis
Issue number5
Publication statusPublished - 2021
Externally publishedYes


  • Growth-fragmentation equations
  • Harris's theorem
  • Long-time behavior of solutions
  • Spectral gap
  • Structured population dynamics


Dive into the research topics of 'Spectral gap for the growth-fragmentation equation via harris's theorem'. Together they form a unique fingerprint.

Cite this