@misc{10481/71504,
year = {2021},
month = {9},
url = {http://hdl.handle.net/10481/71504},
abstract = {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.},
organization = {BERC},
organization = {French Ministry of Research},
organization = {Hausdorff Research Institute for Mathematics

ANR-20-CE40-0015},
organization = {Spanish government},
organization = {European Commission

	639638	EC},
organization = {European Research Council},
organization = {Ministerio de Economía y Competitividad

¡SEV-2017-0718	MINECO},
organization = {European Regional Development Fund},
publisher = {Society for Industrial and Applied Mathematics},
keywords = {Growth-fragmentation equations},
keywords = {Harris's theorem},
keywords = {Spectral gap},
keywords = {Long-time behavior of solutions},
keywords = {Structured population dynamics},
title = {Spectral gap for the growth-fragmentation equation via Harris's theorem},
doi = {10.1137/20M1338654},
author = {Cañizo Rincón, José Alfredo},
}