Mathematical Biosciences and Engineering, 2015, 12(4): 789-801. doi: 10.3934/mbe.2015.12.789.

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

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Global stability for the prion equation with general incidence

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

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

Citation: Pierre Gabriel. Global stability for the prion equation with general incidence. Mathematical Biosciences and Engineering, 2015, 12(4): 789-801. doi: 10.3934/mbe.2015.12.789

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  • 2. Elena Leis, Christoph Walker, Existence of global classical and weak solutions to a prion equation with polymer joining, Journal of Evolution Equations, 2017, 17, 4, 1227, 10.1007/s00028-016-0379-6
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