# Asynchronous exponential growth of the growth-fragmentation equation with unbounded fragmentation rate

Abstract : The objective is to prove the asynchronous exponential growth of the growth-fragmentation equation in large weighted $L^1$ spaces and under general assumptions on the coefficients. The key argument is the creation of moments for the solutions to the Cauchy problem, resulting from the unboundedness of the total fragmentation rate. It allows us to prove the quasi-compactness of the associated (rescaled) semigroup, which in turn provides the exponential convergence toward the projector on the Perron eigenfunction.
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Journal articles

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https://hal.archives-ouvertes.fr/hal-01883140
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Submitted on : Wednesday, July 3, 2019 - 2:47:46 PM
Last modification on : Sunday, June 26, 2022 - 2:39:31 AM

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### Citation

Etienne Bernard, Pierre Gabriel. Asynchronous exponential growth of the growth-fragmentation equation with unbounded fragmentation rate. Journal of Evolution Equations, Springer Verlag, 2020, 20 (2), pp.375-401. ⟨10.1007/s00028-019-00526-4⟩. ⟨hal-01883140v3⟩

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