We consider non‐conservative positive semigroups and obtain necessary and sufficient
conditions for uniform exponential contraction in weighted total variation norm. This ensures …

We study two population models describing the dynamics of interacting neurons, initially
proposed by Pakdaman et al (2010 Nonlinearity 23 55–75) and Pakdaman et al (2014 J …

Motivated by a model for neural networks with adaptation and fatigue, we study a
conservative fragmentation equation that describes the density probability of neurons with …

This work develops further a probabilist approach to the asymptotic behavior of growth-
fragmentation semigroups via the Feynman-Kac formula, which was introduced in a joint …

The dynamics by which polymeric protein filaments divide in the presence of negligible
growth, for example due to the depletion of free monomeric precursors, can be described by …

We consider the linear growth and fragmentation equation: with general coefficients τ, β and
κ. Under suitable conditions (see Doumic Jauffret and Gabriel, 2010 [1]), the first eigenvalue …

In this work we study the coupling of a nonlinear renewal equation to an ordinary differential
equation. We start with existence and uniqueness issues for the coupled equations and, in …

Exponential relaxation to self-similarity for the superquadratic fragmentation equation -
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We investigate an optimal control problem which arises in the optimization of an
amplification technique for misfolded proteins. The improvement of this technique may play …

In this paper we propose some Harris-like criteria in order to study the long time behavior of
general positive and periodic semiflows. These criteria allow us to obtain new existence …