FKPP equation with impulses on unbounded domain

Authors

  • Valaire Yatat Department of Mathematics, Faculty of Science, University of YaoundГ© I, YaoundГ©, Cameroon IRD, UMI 209, UMMISCO, IRD France Nord, F-93143 Bondy, France
  • Yves Dumont CIRAD, UMR AMAP, Pretoria, South Africa AMAP, Univ. Montpellier, CIRAD, CNRS, INRA, IRD, Montpellier, France Department of Mathematics and Applied Mathematics, University of Pretoria, South Africa

DOI:

https://doi.org/10.11145/texts.2017.11.157

Abstract

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.

Author Biographies

Valaire Yatat, Department of Mathematics, Faculty of Science, University of YaoundГ© I, YaoundГ©, Cameroon IRD, UMI 209, UMMISCO, IRD France Nord, F-93143 Bondy, France

Yves Dumont, CIRAD, UMR AMAP, Pretoria, South Africa AMAP, Univ. Montpellier, CIRAD, CNRS, INRA, IRD, Montpellier, France Department of Mathematics and Applied Mathematics, University of Pretoria, South Africa

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Published

2017-12-06

Issue

Section

Conference Proceedings