Traveling Waves for a Bistable Reaction-Diffusion Equation with Delay

Sergei Trofimchuk (1) , Vitaly Volpert (2, 3)

1 Instituto de Matemática y Física - Universidad de Talca
2 DRACULA - Multi-scale modelling of cell dynamics : application to hematopoiesis
3 MMCS - Modélisation mathématique, calcul scientifique

The paper is devoted to a reaction-diffusion equation with delay arising in modeling the immune response. We prove the existence of traveling waves in the bistable case using the Leray--Schauder method. Differently from the previous works, we do not assume here quasi-monotonicity of the delayed reaction term.

Domaines: Equations aux dérivées partielles [math.AP]

Sergei Trofimchuk, Vitaly Volpert. Traveling Waves for a Bistable Reaction-Diffusion Equation with Delay. SIAM Journal on Mathematical Analysis, 2018, 50 (1), pp.1175-1199. ⟨10.1137/17M1115587⟩. ⟨hal-01941474⟩