5 papers
Impact of diffusion mechanisms on persistence and spreading
Nathanaël Boutillon, Yong-Jung Kim, Lionel Roques
We examine a generalized KPP equation with a ``-diffusion", which is a framework that unifies various standard linear diffusion regimes: Fickian diffusion (), Stratonovic…
The principal eigenvalue problem for a strongly anisotropic second-order elliptic operator
Nathanaël Boutillon
We consider an elliptic operator in which the second-order term is very small in one direction. In this regime, we study the behaviour of the principal eigenfunction and of the pri…
Periodic KPP equations: new insights into persistence, spreading, and the role of advection
Nathanaël Boutillon, François Hamel, Lionel Roques
We focus on the persistence and spreading properties for a heterogeneous Fisher-KPP equation with advection. After reviewing the different notions of persistence and spreading spee…
Reaction-diffusion model for a population structured in phenotype and space I -- Criterion for persistence
Nathanaël Boutillon, Luca Rossi
We consider a reaction-diffusion model for a population structured in phenotype. We assume that the population lives in a heterogeneous periodic environment, so that a given phenot…
Qualitative properties of the spreading speed of a population structured in space and in phenotype
Nathanaël Boutillon
We consider a nonlocal Fisher-KPP equation that models a population structured in space and in phenotype. The population lives in a heterogeneous periodic environment: the diffusio…