Global stability for the prion equation with general incidence

Pierre Gabriel (1)

1 LMV - Laboratoire de Mathématiques de Versailles

We consider the so-called prion equation with the general incidence term introduced in [Greer et al., 2007], and we investigate the stability of the steady states. The method is based on the reduction technique introduced in [Gabriel, 2012]. The argument combines a recent spectral gap result for the growth-fragmentation equation in weighted $L^1$ spaces and the analysis of a nonlinear system of three ordinary differential equations.

Mots clés: prion equation; growth-fragmentation equation; spectral gap; self-similarity; long-time behavior; stability

Domaines: Equations aux dérivées partielles [math.AP]

Pierre Gabriel. Global stability for the prion equation with general incidence. 2014. ⟨hal-01002824v1⟩