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Journal of Dynamical and Control Systems

Erschienen in:

05.07.2015

The Asymptotic Behavior of an Age-Cycle Structured Cell Model with Delay

verfasst von: Dongxue Yan, Xianlong Fu

Erschienen in: Journal of Dynamical and Control Systems | Ausgabe 3/2016

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Abstract

This paper is devoted to the study of an age-cycle structured proliferating cell population with delayed boundary condition. Individual cells are distinguished by age and cell cycle length. We consider a general biological rule corresponding to delayed boundary condition. Our focus is on the asymptotic behavior of the system, in particular on the effect of the time lag on the long-term dynamics. To this end, within a semigroup framework, we derive the locally asymptotic stability and asynchrony results, respectively, for the considered population system under some conditions. For our discussion, we use operator matrices, Hille-Yosida operators, spectral analysis, as well as Perron-Frobenius theory.

Vorheriger Artikel Horizontal Holonomy for Affine Manifolds

Nächster Artikel General Expansiveness for Diffeomorphisms from the Robust and Generic Properties

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Bátkai A, Piazzera S. Semigroups and linear partial differential equations with delay. J Math Anal Appl 2001;264:1–20.MathSciNetCrossRefMATH

Bell GI, Anderson EC. Cell growth and division. I. A mathematical model with applications to cell volume distributions in mammalian suspension cultures. Biophys J 1967;7:329–351.CrossRef

Boulanouar M. A mathematical study in the theory of dynamic population. J Math Anal Appl 2001;255:230–259.MathSciNetCrossRefMATH

Boulanouar M. The asymptotic behavior of a structured cell population. J Evol Equ 2011;11:531–552.MathSciNetCrossRefMATH

Boulanouar M. A mathematical analysis of a model of structured population (I). Diff Int Equ 2012;25:821–852.MathSciNetMATH

Boulanouar M. A mathematical analysis of a model of structured population (II). J Dyn Control Syst 2012;18:499–527.MathSciNetCrossRefMATH

Diekmann O. Lecture notes in biomathematies. Vol. 54. Springer Verlag; 1982. p. 90–96.

Engel KJ. Operator matrices and systems of evolution equations. RIMS Kokyuroku 1996;966:61–80.MathSciNetMATH

Engel KJ, Nagel R. One-parameter semigroups for linear evolution equations: Springer; 2000.

10.

Gurtin ME, MacCamy RM. Nonlinear age-dependent population dynamics. Arch Ration Mech Anal 1974;54:281–300.MathSciNetCrossRefMATH

11.

Greiner G. A typical Perron-Frobenius theorem with applications to an age-dependent population equation, Lect. Notes in Math., Vol. 1076. Springer; 1984. p. 86–100.

12.

Greiner G. Perturbing the boundary conditions of a generator. Houston J Math 1987;13:213–229.MathSciNetMATH

13.

Greiner G, Nagel R. Growth of cell populations via one-parameter semigroups of positive operators, Mathematics Applied to Science (New Orleans, La, 1986);1988:79–105.

14.

Gyllenberg M, Webb GF. Asynchronous exponential growth of semigroups of nonlinear operators. J Math Anal Appl 1992;167:443–467.MathSciNetCrossRefMATH

15.

Latrach K, Mokhtar-Kharroubi M. On an unbounded linear operator arising in the theory of growing cell population. J Math Anal Appl 1997;211:273–294.MathSciNetCrossRefMATH

16.

Lebowitz JL, Rubinow SI. A theory for the age and generation time distribution of a microbial population. J Math Biol 1974;1:17–36.MathSciNetCrossRefMATH

17.

Nagel R, (ed). One-Parameter Semigroups of Positive Operators, Lect. Notes in Math. 1184. Springer-Verlag; 1986.

18.

Nagel R. The spectrum of unbounded operator matrices with non-diagonal domain. J Funct Anal 1990;89:291–302.MathSciNetCrossRefMATH

19.

Nagel R, Nickel G, Romanelli S. Identification of extrapolation spaces for unbounded operators. Quaest Math 1996;19:83–100.MathSciNetCrossRefMATH

20.

Prüss J. Equilibrium solutions of age-specific population dynamics of several species. J Math Biol 1981;11:65–84.MathSciNetCrossRefMATH

21.

Prüss J, Schappacher W. Semigroup methods for age-structured population dynamics. Vieweg: Jahrbuch Uberblicke Mathematik; 1994, pp. 74–90.MATH

22.

Pazy A. Semigroups of linear operators and applications to partial differential equations. New York: Springer; 1983.CrossRefMATH

23.

Pizzera S, Tonetto L. Asynchronous exponential growth for an age dependent population equation with delayed birth process. J Evol Equ 2005;5:61–77.MathSciNetCrossRefMATH

24.

Rhandi A, Schnaubelt R. Asymptotic behavior of a non-autonomous population equation with diffusion in L ¹. Discr Cont Dyn Syst 1999;5:663–683.MathSciNetCrossRefMATH

25.

Weis L. The stability of positive semigroups on L _p spaces. Proc Amer Math Soc 1995;123:3089–3094.MathSciNetMATH

26.

Webb GF. Theory of nonlinear age-dependent population dynamics. Marcell Dekker; 1985.

27.

Webb GF. A model of proliferating cell populations with inherited cycle length. T Math Biol 1986;23:269–282.MathSciNetCrossRefMATH

28.

Webb GF. A semigroup proof of the Sharpe-Lotka theorem. Lect. Notes Math. Springer. 1983;1076:254–268.

29.

Webb GF. Dynamics of structured populations with inherited properties. Comput Math Appl 1987;13:749–757.MathSciNetCrossRefMATH

Titel: The Asymptotic Behavior of an Age-Cycle Structured Cell Model with Delay
verfasst von: Dongxue Yan
Xianlong Fu
Publikationsdatum: 05.07.2015
Verlag: Springer US
Erschienen in: Journal of Dynamical and Control Systems / Ausgabe 3/2016
Print ISSN: 1079-2724
Elektronische ISSN: 1573-8698
DOI: https://doi.org/10.1007/s10883-015-9285-4

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