Existence of waves for a reaction–diffusion–dispersion system

Moitri Sen (1) , Vitaly Volpert (2, 3) , Vitali Vougalter (4)

1 NIT - National Institute of Technology [Patna]
2 DRACULA - Multi-scale modelling of cell dynamics : application to hematopoiesis
3 MMCS - Modélisation mathématique, calcul scientifique
4 Department of Mathematics [University of Toronto]

Existence of travelling waves is studied for a bistable reaction–diffusion system of equations with linear integral terms (dispersion) and with some conditions on the nonlinearity. The proof is based on the Leray–Schauder method using the topological degree theory for Fredholm and proper operators with the zero index and a priori estimates of solutions in properly chosen weighted spaces.

Domaines: Equations aux dérivées partielles [math.AP]

Moitri Sen, Vitaly Volpert, Vitali Vougalter. Existence of waves for a reaction–diffusion–dispersion system. Nonlinear Analysis: Theory, Methods and Applications, 2019, 180, pp.52-66. ⟨10.1016/j.na.2018.09.011⟩. ⟨hal-01941461⟩