Global stability for the prion equation with general incidence

Pierre Gabriel

doi:10.3934/mbe.2015.12.789

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

Pierre Gabriel

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

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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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This article has been cited by:

1. Étienne Bernard, Pierre Gabriel, Asymptotic behavior of the growth-fragmentation equation with bounded fragmentation rate, Journal of Functional Analysis, 2017, 272, 8, 3455, 10.1016/j.jfa.2017.01.009
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
3. Juan Calvo, Marie Doumic, Benoît Perthame, Long-Time Asymptotics for Polymerization Models, Communications in Mathematical Physics, 2018, 363, 1, 111, 10.1007/s00220-018-3218-5
4. Elena Leis, Christoph Walker, Uniqueness of weak solutions to a prion equation with polymer joining, Analysis, 2017, 37, 2, 10.1515/anly-2016-0034

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Copyright Info: 2015, Pierre Gabriel, licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution Licese (http://creativecommons.org/licenses/by/4.0)

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