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Journal Articles Communications in Mathematical Sciences Year : 2017

On the variations of the principal eigenvalue with respect to a parameter in growth-fragmentation models

Abstract

We study the variations of the principal eigenvalue associated to a growth-fragmentation-death equation with respect to a parameter acting on growth and fragmentation. To this aim, we use the probabilistic individual-based interpretation of the model. We study the variations of the survival probability of the stochastic model, using a generation by generation approach. Then, making use of the link between the survival probability and the principal eigenvalue established in a previous work, we deduce the variations of the eigenvalue with respect to the parameter of the model.
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Dates and versions

hal-01254053 , version 1 (11-01-2016)
hal-01254053 , version 2 (03-02-2016)
hal-01254053 , version 3 (23-01-2017)

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Cite

Fabien Campillo, Nicolas Champagnat, Coralie Fritsch. On the variations of the principal eigenvalue with respect to a parameter in growth-fragmentation models. Communications in Mathematical Sciences, 2017, 15 (7), pp.1801-1819. ⟨10.4310/CMS.2017.v15.n7.a1⟩. ⟨hal-01254053v3⟩
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