Existence of Pulses for Local and Nonlocal Reaction-Diffusion Equations

Nathalie Eymard (1) , Vitaly Volpert (2, 1) , Vitali Vougalter (3)

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

Reaction-diffusion equations with a space dependent nonlinearity are considered on the whole axis. Existence of pulses, stationary solutions which vanish at infinity, is studied by the Leray-Schauder method. It is based on the topological degree for Fredholm and proper operators with the zero index in some special weighted spaces and on a priori estimates of solutions in these spaces. Existence of solutions is related to the speed of travelling wave solutions for the corresponding autonomous equations with the limiting nonlinearity.

Mots clés: existence of pulse solutions; reaction-diffusion equation; Leray-Schauder method AMS subject classification: 35K57; 35A16; 92D15

Domaines: Equations aux dérivées partielles [math.AP]

Nathalie Eymard, Vitaly Volpert, Vitali Vougalter. Existence of Pulses for Local and Nonlocal Reaction-Diffusion Equations. Journal of Dynamics and Differential Equations, 2015, ⟨10.1007/s10884-015-9487-1⟩. ⟨hal-01237744⟩