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 the long-time behavior of the growth-fragmentation equation, a nonlocal linear
evolution equation describing a wide range of phenomena in structured population …

The evolution of mutualism between host and symbiont communities plays an essential role
in maintaining ecosystem function and should therefore have a profound effect on their …

Neural network dynamics emerge from the interaction of spiking cells. One way to formulate
the problem is through a theoretical framework inspired by ideas coming from statistical …

In this article, we analyse the non-local model:∂ t U (t, x)= J⋆ U (t, x)− U (t, x)+ f (x− ct, U (t,
x)) for t> 0, and x∈ R, where J is a positive continuous dispersal kernel and f (x, s) is a …

In this work, we revisit the Krein-Rutman theory for semigroups of positive operators in a
Banach lattice framework and we provide some very general, efficient and handy results …

This Review concerns recent results on the quantitative study of convergence toward the
stationary state for spatially inhomogeneous kinetic equations. We focus on analytical …

We consider nonlinear mutation selection models, known as replicator-mutator equations in
evolutionary biology. They involve a nonlocal mutation kernel and a confining fitness …

We study the long time behavior of an asymmetric size-structured measure-valued growth-
fragmentation branching process that models the dynamics of a population of cells taking …

Many populations can somehow adapt to rapid environmental changes. To understand this
fast evolution, we investigate the genealogy of individuals inside those populations. More …