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; stability; long-time behavior; self-similarity; spectral gap; growth-fragmentation equation

Domaines: Equations aux dérivées partielles [math.AP]

Pierre Gabriel. Global stability for the prion equation with general incidence. Mathematical Biosciences and Engineering, 2015, Special issue dedicated to the 70th birthday of Glenn F. Webb, 12 (4), pp.789-801. ⟨10.3934/mbe.2015.12.789⟩. ⟨hal-01002824v2⟩