Estimate of the travelling wave speed for an integro-differential equation

Nikolay Bessonov (1) , Anne Beuter (2) , Sergei Trofimchuk (3) , Vitaly Volpert (4, 5)

1 IPME - Institute of Mechanical Engineering Problems [St. Petersburg]
2 IMS - Laboratoire de l'intégration, du matériau au système
3 Instituto de Matemática y Física - Universidad de Talca
4 DRACULA - Multi-scale modelling of cell dynamics : application to hematopoiesis
5 MMCS - Modélisation mathématique, calcul scientifique

Travelling waves for nonlocal reaction–diffusion equations are studied. The minimax representation of the wave speed is obtained. It is used to obtain analytical estimates and asymptotic values of the speed. Two regimes of wave propagation are identified. One of them is dominated by diffusion and another one by the nonlocal interaction.

Domaines: Equations aux dérivées partielles [math.AP]

Nikolay Bessonov, Anne Beuter, Sergei Trofimchuk, Vitaly Volpert. Estimate of the travelling wave speed for an integro-differential equation. Applied Mathematics Letters, 2019, 88, pp.103-110. ⟨10.1016/j.aml.2018.07.037⟩. ⟨hal-01941455⟩