| Issue |
Math. Model. Nat. Phenom.
Volume 17, 2022
|
|
|---|---|---|
| Article Number | 17 | |
| Number of page(s) | 31 | |
| DOI | https://doi.org/10.1051/mmnp/2022021 | |
| Published online | 17 June 2022 | |
Traveling waves for reaction-diffusion PDE coupled to difference equation with nonlocal dispersal term and time delay
1
Inria, CNRS UMR 5208, Institut Camille Jordan, Université Lyon 1, 69200 Villeurbanne, France
2
Laboratoire d’Analyse Nonlinéaire et Mathématiques Appliquées, University of Tlemcen, Tlemcen 13000, Algeria
3
Institute of Fundamental Technological Research, Polish Academy of Sciences, Pawińskiego 5B, 02-106 Warsaw, Poland
* Corresponding author: mostafa.adimy@gmail.com
Received:
5
January
2022
Accepted:
20
May
2022
We consider a class of biological models represented by a system composed of reactiondiffusion PDE coupled with difference equations (renewal equations) in n-dimensional space, with nonlocal dispersal terms and implicit time delays. The difference equation generally arises, by means of the method of characteristics, from an age-structured partial differential system. Using upper and lower solutions, we study the existence of monotonic planar traveling wave fronts connecting the extinction state to the uniform positive state. The corresponding minimum wave speed is also obtained. In addition, we investigate the effect of the parameters on this minimum wave speed and we give a detailed analysis of its asymptotic behavior.
Mathematics Subject Classification: 35K20 / 35Q92 / 92D30
Key words: Planar monotone traveling wave front / Reaction-diffusion PDE with delay / Difference equation / Monostable equation
© The authors. Published by EDP Sciences, 2022
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