Skip to Main content Skip to Navigation
Theses

Propagation phenomena and reaction–diffusion systems for population dynamics in homogeneous or periodic media

Abstract : This thesis is dedicated to the study of propagation properties of various reaction–diffusion systems coming from population dynamics. In the first part, we study the strong competition limit of competition–diffusion systems with two species. Thanks to the spatial segregation, we determine the sign of the speed of the bistable traveling wave. The generalization to bistable pulsating fronts in spatially periodic media is then considered in order to study the role of spatial heterogeneity. We find a condition sufficient for the existence of such fronts as well as a condition sufficient for the existence of stable steady states which might on the contrary block the propagation. Then we show that whenever a family of strongly competing pulsating fronts exists, we can establish a result very similar to the one obtained in homogeneous media. In the second part, systems of KPP type with any number of species are considered. We study the existence of steady states and traveling waves, the qualitative properties of these solutions as well as the asymptotic speed of spreading of certain solutions of the Cauchy problem. This settles several open questions on the prototypical KPP systems that are mutation–competition–diffusion systems. In the third part, we go back to competition–diffusion systems with two species. Considering this time the monostable case, we study the asymptotic speeds of spreading of certain solutions of the Cauchy problem. By so doing, we show the existence of propagating terraces describing the invasion of an uninhabited territory by a weak but fast competitor followed by the invasion by a strong but slow competitor.
Document type :
Theses
Complete list of metadatas

Cited literature [169 references]  Display  Hide  Download

https://tel.archives-ouvertes.fr/tel-02355216
Contributor : Abes Star :  Contact
Submitted on : Friday, November 8, 2019 - 10:43:29 AM
Last modification on : Friday, August 21, 2020 - 5:44:21 AM
Long-term archiving on: : Sunday, February 9, 2020 - 9:28:50 PM

File

these_archivage_3367474.pdf
Version validated by the jury (STAR)

Identifiers

  • HAL Id : tel-02355216, version 1

Citation

Léo Girardin. Propagation phenomena and reaction–diffusion systems for population dynamics in homogeneous or periodic media. Dynamical Systems [math.DS]. Sorbonne Université, 2018. English. ⟨NNT : 2018SORUS147⟩. ⟨tel-02355216⟩

Share

Metrics

Record views

134

Files downloads

178