Mathematical Biosciences and Engineering (MBE)

Global stability for the prion equation with general incidence

Pages: 789 - 801, Volume 12, Issue 4, August 2015      doi:10.3934/mbe.2015.12.789

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Pierre Gabriel - Laboratoire de Mathématiques de Versailles, CNRS UMR 8100, Université de Versailles Saint-Quentin-en-Yvelines, 45 Avenue de États-Unis, 78035 Versailles cedex, France (email)

Abstract: We consider the so-called prion equation with the general incidence term introduced in [14], and we investigate the stability of the steady states. The method is based on the reduction technique introduced in [11]. 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.

Keywords:  Prion equation, growth-fragmentation equation, spectral gap, self-similarity, long-time behavior, stability.
Mathematics Subject Classification:  Primary: 92D25; Secondary: 35B35, 35B40, 35Q92, 45K05.

Received: May 2014;      Accepted: January 2015;      Available Online: April 2015.