Spectral gap for the growth-fragmentation equation via Harris's theorem Cañizo Rincón, José Alfredo Growth-fragmentation equations Harris's theorem Spectral gap Long-time behavior of solutions Structured population dynamics The work of the first and third authors was supported by the project MTM2017- 85067-P, funded by the Spanish government and the European Regional Development Fund and they gratefully acknowledge the support of the Hausdorff Research Institute for Mathematics (Bonn), through the Junior Trimester Program on Kinetic Theory. The work of the second author was supported by the ANR project NOLO, grant ANR-20-CE40-0015, funded by the French Ministry of Research. The work of the third author was also supported by the Basque Government through the BERC 2018-2021 program, by the Spanish Ministry of Economy and Competitiveness MINECO: BCAM Severo Ochoa excellence accreditation SEV-2017-0718, by the ``la Caixa"" Foundation, and by the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme grant 639638. 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. 2021-11-15T08:13:05Z 2021-11-15T08:13:05Z 2021-09-16 journal article Cañizo, J. A., Gabriel, P., & Yoldas, H. (2021). Spectral gap for the growth-fragmentation equation via Harris's Theorem. SIAM Journal on Mathematical Analysis, 53(5), 5185-5214. DOI. [10.1137/20M1338654] http://hdl.handle.net/10481/71504 10.1137/20M1338654 eng info:eu-repo/grantAgreement/EC/H2020/639638 http://creativecommons.org/licenses/by-nc-nd/3.0/es/ open access Atribución-NoComercial-SinDerivadas 3.0 España Society for Industrial and Applied Mathematics