Traveling waves for reaction-diffusion PDE coupled to difference equation with nonlocal dispersal term and time delay

Mostafa Adimy¹ ; Abdennasser Chekroun² ; Bogdan Kazmierczak³

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

Mathematical modelling of natural phenomena, Tome 17 (2022), article no. 17

Résumé

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.

Détail

DOI : 10.1051/mmnp/2022021

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