Article Dans Une Revue Journal of Evolution Equations Année : 2020

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

Résumé

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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Dates et versions

hal-01883140 , version 1 (27-09-2018)
hal-01883140 , version 2 (22-10-2018)
hal-01883140 , version 3 (03-07-2019)

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