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Global existence and asymptotic behavior for a nonlinear degenerate SIS model

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Języki publikacji
EN
Abstrakty
EN
In this paper we investigate the global existence and asymptotic behavior of a reaction diffusion system with degenerate diffusion arising in the modeling and the spatial spread of an epidemic disease.
Rocznik
Strony
615--630
Opis fizyczny
Bibliogr. 16 poz.
Twórcy
autor
  • USTHB, Laboratoire AMNEDP, Faculté des Mathématiques, BP 32 El alia Bab Ezzouar, 16111, Algiers, Algeria
Bibliografia
  • [1] T. Ali Ziane, Etude de la régularité pour un problème d’évolution dégénéré en dimension supérieure de l’espace, Magister’s Thesis, U.S.T.H.B. Alger, 1993.
  • [2] T. Ali Ziane, L. Hadjadj, M.S. Moulay, Nonlinear reaction diffusion systems of degenerate parabolic type, Port. Math. 66 (2009) 3, 373–400.
  • [3] T. Ali Ziane, M. Langlais, Degenerate diffusive Seir model with logistic population control, Acta Math. Univ. Comenian., (N.S.) 75 (2006) 2, 185–198.
  • [4] T. Ali Ziane, M. Langlais, Global existence and asymptotic behaviour for a degenerate diffusive SEIR model, Electron. J. Qual. Theory Differ. Equ. 2 (2005), 1–15.
  • [5] T. Ali Ziane, M.S. Moulay, Global existence and asymptotic behaviour for a system of degenerate evolution equations, Maghreb Math. Rev. 9 (2000), 9–22.
  • [6] V. Capasso, G. Serio, A generalization of the Kermack-McKendrick deterministic epidemic model, Math. Biosci. 42 (1978) 1–2, 43–61.
  • [7] E. Di Benedetto, Continuity of weak solutions to a general porous medium equation, Indiana Univ. Math. J. 32 (1983) 1, 83–118.
  • [8] W. Fitzgibbon, M. Langlais, Diffusive SEIR models with logistic population control, Comm. Appl. Nonlinear Anal. 4 (1997) 3, 1–16.
  • [9] W. Fitzgibbon, M. Langlais, J. Morgan, Eventually uniform bounds for a class of quasipositive reaction diffusion systems, Japan J. Indust. Appl. Math. 16 (1999) 2, 225–241.
  • [10] W. Fitzgibbon, J.J. Morgan, S.J. Waggoner, A quasilinear system modeling the spread of infectious disease, Rocky Mountain J. Math. 22 (1992) 2, 579–592.
  • [11] W.O. Kermack, A.G. McKendrick, Contribution to the mathematical theory of epidemics. II-the problem of endemicity, Proc. Roy. Soc. Edin. A 138 (1932), 55–83.
  • [12] O.A. Ladyzenskaja, V.A. Solonnikov, N.N. Ural’ceva, Linear and Quasilinear Equation of Parabolic Type, Translations of Mathematical Monographs, Vol. 23, American Mathematical Society, Providence, R.I. 1967.
  • [13] L. Maddalena, Existence, uniqueness and qualitative properties of the solution of a degenerate nonlinear parabolic system, J. Math. Anal. Appl. 127 (1987) 2, 443–458.
  • [14] A. Okubo, Diffusion and ecological problems: mathematical models, An extended version of the Japanese edition, Ecology and diffusion. Translated by G.N. Parker. Biomathematics, 10. Springer-Verlag, Berlin-New York, 1980.
  • [15] O.A. Oleinik, A.S. Kalashnikov, C. Yui-Lin, The Cauchy problem and boundary problems for equations of the type of non-stationary filtration, Izv. Akad. Nauk SSSR. Ser. Mat. 22 (1958), 667–704.
  • [16] J. Smoller, Shock Waves and Reaction-Diffusion Equations, 2nd ed., Springer-Verlag, New York, 1994.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-526b806f-fb64-48a9-8f52-c91304839df8
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