\`x^2+y_1+z_12^34\`
Advanced Search
Article Contents
Article Contents

Global classical and weak solutions of the prion proliferation model in the presence of chaperone in a banach space

  • * Corresponding author: Kapil Kumar Choudhary

    * Corresponding author: Kapil Kumar Choudhary 
Abstract Full Text(HTML) Related Papers Cited by
  • The present work is based on the coupling of prion proliferation system together with chaperone which consists of two ODEs and a partial integro-differential equation. The existence and uniqueness of a positive global classical solution of the system is proved for the bounded degradation rates by the idea of evolution system theory in the state space $ \mathbb{R} \times \mathbb{R} \times L_{1}(Z,zdz). $ Moreover, the global weak solutions for unbounded degradation rates are discussed by weak compactness technique.

    Mathematics Subject Classification: 35R09, 47D06.

    Citation:

    \begin{equation} \\ \end{equation}
  • 加载中
  • [1] H. Amann, Linear and Quasilinear Parabolic Problems: Abstract Linear Theory, Birkhäuser, Basel, 1995. doi: 10.1007/978-3-0348-9221-6.
    [2] J. Banasiak and L. Arlotti, Perturbations of Positive Semigroups with Applications, Springer Monographs in Mathematics. Springer-Verlag London, Ltd., London, 2006.
    [3] R. E. Edwards, Functional Analysis: Theory and Applications, Corrected reprint of the 1965 original. Dover Publications, Inc., New York, 1995.
    [4] H. EnglerJ. Pruss and G. F. Webb, Analysis of a model for the dynamics of prions II, J. Math. Anal. Appl., 324 (2006), 98-117.  doi: 10.1016/j.jmaa.2005.11.021.
    [5] P. Gabriel, Global stability for the prion equation with general incidence, Math. Biosc. Eng., 12 (2015), 789-801.  doi: 10.3934/mbe.2015.12.789.
    [6] M. L. GreerP. van den DriesscheL. Wang and G. F. Webb, Effects of general incidence and polymer joining on nucleated polymerzation in a model of prion proliferation, SIAM J. Appl. Math., 68 (2007), 154-170.  doi: 10.1137/06066076X.
    [7] M. L. GreerL. Pujo-Menjouet and G. F. Webb, A mathematical analysis of the dynamics of prion proliferation, J. Theoretial Biology, 242 (2006), 598-606.  doi: 10.1016/j.jtbi.2006.04.010.
    [8] R. Kumar and P. Murali, Modeling and analysis of prion dynamics in the presence of a chaperone, Mathematical Biosciences, 213 (2008), 50-55.  doi: 10.1016/j.mbs.2008.02.002.
    [9] R. KumarK. K. Choudhary and R. Kumar, Study of the solution of a semilinear evolution equation of a prion proliferation model in the presence of chaperone in a product space, Math. Meth. Appl. Sci., 44 (2021), 1942-1955.  doi: 10.1002/mma.6894.
    [10] M. LachowiczP. Laurençot and D. Wrzosek, On the Oort–Hulst–Safronov coagulation equation and its relation to the Smoluchowski equation, SIAM J. Math. Anal., 34 (2003), 1399-1421.  doi: 10.1137/S0036141002414470.
    [11] P. Laurençot and C. Walker, Well-posedness for a model of prion proliferation dynamics, J. Evolution Equations, 7 (2007), 241-264.  doi: 10.1007/s00028-006-0279-2.
    [12] E. Leis and C. Walker, Existence of global classical and weak solutions to a prion equation with polymer joining, J. Evolution Equations, 17 (2017), 1227-1258.  doi: 10.1007/s00028-016-0379-6.
    [13] A. Pazy, Semigroups of Linear Operators and Applications to Partial Differential Equations, Applied Mathematical Sciences, 44. Springer-Verlag, New York, 1983. doi: 10.1007/978-1-4612-5561-1.
    [14] J. PrussL. Pujo-MenjouetG. F. Webb and R. Zacher, Analysis of a model for the dynamics of prions, Discrete Contin. Dyn. Syst. Ser. B, 6 (2006), 225-235.  doi: 10.3934/dcdsb.2006.6.225.
    [15] G. Simonett and C. Walker, On the solvability of a mathematical model for prion proliferation, J. Math. Anal. Appl., 324 (2006), 580-603.  doi: 10.1016/j.jmaa.2005.12.036.
    [16] I. I. Vrabie, Compactness Methods for Nonlinear Evolutions, With a foreword by A. Pazy. Second edition. Pitman Monographs and Surveys in Pure and Applied Mathematics, 75. Longman Scientific & Technical, Harlow; copublished in the United States with John Wiley & Sons, Inc., New York, 1995.
  • 加载中
SHARE

Article Metrics

HTML views(1913) PDF downloads(483) Cited by(0)

Access History

Other Articles By Authors

Catalog

    /

    DownLoad:  Full-Size Img  PowerPoint
    Return
    Return