Global stability for the prion equation with general incidence

Pierre Gabriel

doi:10.3934/mbe.2015.12.789

Article Contents

2015, Volume 12, Issue 4: 789-801. Doi: 10.3934/mbe.2015.12.789 open access

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Global stability for the prion equation with general incidence

Pierre Gabriel^1,

1.
Laboratoire de Mathématiques de Versailles, CNRS UMR 8100, Université de Versailles Saint-Quentin-en-Yvelines, 45 Avenue de États-Unis, 78035 Versailles cedex

Received: April 30, 2014

Revised: December 31, 2014

Published: March 2015

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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.

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Mathematics Subject Classification: Primary: 92D25; Secondary: 35B35, 35B40, 35Q92, 45K05.

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