FKPP equation with impulses on unbounded domain

Yatat Valaire, Dumont Yves. 2018. FKPP equation with impulses on unbounded domain. In : Mathematical Methods and Models in Biosciences. International conference BIOMATH 2017. Roumen Anguelov (ed.), Miroslaw Lachowicz (ed.). Sofia : Biomath Forum, 1-21. ISBN 978-619-7451-00-9 International conference BIOMATH 2017, Kruger Park, Afrique du Sud, 25 Juin 2017/30 Juin 2017.

Url - éditeur : http://www.biomathforum.org/biomath/index.php/texts/article/view/texts.2017.11.157

Résumé : This paper deals with the problem of travelling wave solutions in a scalar impulsive FKPP-like equation. It is a first step of a more general study that aims to address existence of travelling wave solutions for systems of impulsive reaction-diffusion equations that model ecological systems dynamics such as fire-prone savannas. Using results on scalar recursion equations, we show existence of populated vs. extinction travelling waves invasion and compute an explicit expression of their spreading speed (characterized as the minimal speed of such travelling waves). In particular, we find that the spreading speed explicitly depends on the time between two successive impulses. In addition, we carry out a comparison with the case of time-continuous events. We also show that depending on the time between two successive impulses, the spreading speed with pulse events could be lower, equal or greater than the spreading speed in the case of time-continuous events. Finally, we apply our results to a model of fire-prone grasslands and show that pulse fires event may slow down the grassland vs. bare soil invasion speed.

Mots-clés libres : Partial differential equation, Impulsive event, Travelling wave, Savannah, Impulsive fire, Numerical simulations

Classification Agris : U10 - Informatique, mathématiques et statistiques
H50 - Troubles divers des plantes
000 - Autres thèmes

Auteurs et affiliations

• Yatat Valaire, Université de Yaoundé 1 (CMR)
• Dumont Yves, CIRAD-BIOS-UMR AMAP (FRA) ORCID: 0000-0003-4817-685X

Source : Cirad-Agritrop (https://agritrop.cirad.fr/586309/)

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