Global stability for the prion equation with general incidence

  • Received: 01 May 2014 Accepted: 29 June 2018 Published: 01 April 2015
  • MSC : Primary: 92D25; Secondary: 35B35, 35B40, 35Q92, 45K05.

  • 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.

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

    Related Papers:

  • 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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    [1] Kinetic Related Models, 6 (2013), 219-243.
    [2] Comm. Appl. Ind. Math., 1 (2010), 299-308.
    [3] J. Math. Pures Appl., 96 (2011), 334-362.
    [4] J. Biol. Dyn., 4 (2010), 28-42.
    [5] Math. Biosci., 217 (2009), 88-99.
    [6] Comm. Math. Sci., 7 (2009), 839-865.
    [7] Math. Models Methods Appl. Sci., 20 (2010), 757-783.
    [8] J. Math. Anal. Appl., 324 (2006), 98-117.
    [9] Ann. Inst. H. Poincaré Anal. Non Linéaire, 22 (2005), 99-125.
    [10] Math. Comput. Modelling, 53 (2011), 1451-1456.
    [11] Commun. Math. Sci., 10 (2012), 787-820.
    [12] Appl. Math. Lett., 27 (2014), 74-78.
    [13] J. Theoret. Biol., 242 (2006), 598-606.
    [14] SIAM J. Appl. Math., 68 (2007), 154-170.
    [15] Nature, 215 (1967), 1043-1044.
    [16] Cell, 73 (1993), 1055-1058.
    [17] Commun. Math. Sci., 7 (2009), 503-510.
    [18] J. Evol. Equ., 7 (2007), 241-264.
    [19] Biophysical Chemistry, 77 (1999), 139-152.
    [20] J. Math. Pures Appl., 84 (2005), 1235-1260.
    [21] arXiv:1310.7773.
    [22] J. Differential Equations, 210 (2005), 155-177.
    [23] Science, 216 (1982), 136-144.
    [24] Dis. Cont. Dyn. Sys. Ser. B, 6 (2006), 225-235.
    [25] Nature, 437 (2005), 257-261.
    [26] J. Math. Anal. Appl., 324 (2006), 580-603.
    [27] American Mathematical Society, Providence, RI, 1995.
    [28] in Proceedings of the Sixth Mississippi State-UBA Conference on Differential Equations and Computational Simulations, 15 (2007), 387-397.
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