American Institute of Mathematical Sciences

Advanced
  • Previous Article
    Existence and multiplicity of positive solutions for nonlinear boundary value problems driven by the scalar $p$-Laplacian
  • CPAA Home
  • This Issue
  • Next Article
    Compressible Navier-Stokes equations with vacuum state in one dimension
December  2004, 3(4): 695-727. doi: 10.3934/cpaa.2004.3.695

Eventual compactness for semiflows generated by nonlinear age-structured models

P. Magal 1, and  H. R. Thieme 2,

1. 

Department of Mathematics, Université du Havre, 76058 Le Havre, France
2. 

Department of Mathematics, Arizona State University, Tempe, AZ 85287-1804, United States

Received  November 2003 Revised  June 2004 Published  September 2004

In this paper we investigate compactness properties for a semiflow generated by a semi-linear equation with non-dense domain. We start with the non-homogeneous linear case, and we derive some abstract conditions for non-autonomous semilinear equations. Then we investigate a special situation which is well adapted for age-structured equations. We conclude the paper by applying the abstract results to an age-structured model with an additional structure.
Keywords: Age structured models, attractors, asymptotically smooth semiflow..
Mathematics Subject Classification: 34Gxx, 47H20, 47J35, 58D25, 92D2.
Citation: P. Magal, H. R. Thieme. Eventual compactness for semiflows generated by nonlinear age-structured models. Communications on Pure & Applied Analysis, 2004, 3 (4) : 695-727. doi: 10.3934/cpaa.2004.3.695
[1]

Yicang Zhou, Paolo Fergola. Dynamics of a discrete age-structured SIS models. Discrete & Continuous Dynamical Systems - B, 2004, 4 (3) : 841-850. doi: 10.3934/dcdsb.2004.4.841
[2]

Zhihua Liu, Rong Yuan. Takens–Bogdanov singularity for age structured models. Discrete & Continuous Dynamical Systems - B, 2020, 25 (6) : 2041-2056. doi: 10.3934/dcdsb.2019201
[3]

Yicang Zhou, Zhien Ma. Global stability of a class of discrete age-structured SIS models with immigration. Mathematical Biosciences & Engineering, 2009, 6 (2) : 409-425. doi: 10.3934/mbe.2009.6.409
[4]

Zhihua Liu, Pierre Magal, Shigui Ruan. Oscillations in age-structured models of consumer-resource mutualisms. Discrete & Continuous Dynamical Systems - B, 2016, 21 (2) : 537-555. doi: 10.3934/dcdsb.2016.21.537
[5]

Andrea Franceschetti, Andrea Pugliese, Dimitri Breda. Multiple endemic states in age-structured $SIR$ epidemic models. Mathematical Biosciences & Engineering, 2012, 9 (3) : 577-599. doi: 10.3934/mbe.2012.9.577
[6]

Zhilan Feng, Qing Han, Zhipeng Qiu, Andrew N. Hill, John W. Glasser. Computation of $\mathcal R $ in age-structured epidemiological models with maternal and temporary immunity. Discrete & Continuous Dynamical Systems - B, 2016, 21 (2) : 399-415. doi: 10.3934/dcdsb.2016.21.399
[7]

Yingli Pan, Ying Su, Junjie Wei. Bistable waves of a recursive system arising from seasonal age-structured population models. Discrete & Continuous Dynamical Systems - B, 2019, 24 (2) : 511-528. doi: 10.3934/dcdsb.2018184
[8]

B. San Martín, Kendry J. Vivas. Asymptotically sectional-hyperbolic attractors. Discrete & Continuous Dynamical Systems - A, 2019, 39 (7) : 4057-4071. doi: 10.3934/dcds.2019163
[9]

Fadia Bekkal-Brikci, Khalid Boushaba, Ovide Arino. Nonlinear age structured model with cannibalism. Discrete & Continuous Dynamical Systems - B, 2007, 7 (2) : 201-218. doi: 10.3934/dcdsb.2007.7.201
[10]

P.E. Kloeden, Desheng Li, Chengkui Zhong. Uniform attractors of periodic and asymptotically periodic dynamical systems. Discrete & Continuous Dynamical Systems - A, 2005, 12 (2) : 213-232. doi: 10.3934/dcds.2005.12.213
[11]

Jianxin Yang, Zhipeng Qiu, Xue-Zhi Li. Global stability of an age-structured cholera model. Mathematical Biosciences & Engineering, 2014, 11 (3) : 641-665. doi: 10.3934/mbe.2014.11.641
[12]

Ryszard Rudnicki, Radosław Wieczorek. On a nonlinear age-structured model of semelparous species. Discrete & Continuous Dynamical Systems - B, 2014, 19 (8) : 2641-2656. doi: 10.3934/dcdsb.2014.19.2641
[13]

Fred Brauer. A model for an SI disease in an age - structured population. Discrete & Continuous Dynamical Systems - B, 2002, 2 (2) : 257-264. doi: 10.3934/dcdsb.2002.2.257
[14]

Janet Dyson, Eva Sánchez, Rosanna Villella-Bressan, Glenn F. Webb. An age and spatially structured model of tumor invasion with haptotaxis. Discrete & Continuous Dynamical Systems - B, 2007, 8 (1) : 45-60. doi: 10.3934/dcdsb.2007.8.45
[15]

Jacek Banasiak, Aleksandra Falkiewicz. A singular limit for an age structured mutation problem. Mathematical Biosciences & Engineering, 2017, 14 (1) : 17-30. doi: 10.3934/mbe.2017002
[16]

Mohammed Nor Frioui, Tarik Mohammed Touaoula, Bedreddine Ainseba. Global dynamics of an age-structured model with relapse. Discrete & Continuous Dynamical Systems - B, 2020, 25 (6) : 2245-2270. doi: 10.3934/dcdsb.2019226
[17]

Hongyong Cui. Convergences of asymptotically autonomous pullback attractors towards semigroup attractors. Discrete & Continuous Dynamical Systems - B, 2019, 24 (8) : 3525-3535. doi: 10.3934/dcdsb.2018276
[18]

A. Ducrot. Travelling wave solutions for a scalar age-structured equation. Discrete & Continuous Dynamical Systems - B, 2007, 7 (2) : 251-273. doi: 10.3934/dcdsb.2007.7.251
[19]

Geni Gupur, Xue-Zhi Li. Global stability of an age-structured SIRS epidemic model with vaccination. Discrete & Continuous Dynamical Systems - B, 2004, 4 (3) : 643-652. doi: 10.3934/dcdsb.2004.4.643
[20]

Xi Huo. Modeling of contact tracing in epidemic populations structured by disease age. Discrete & Continuous Dynamical Systems - B, 2015, 20 (6) : 1685-1713. doi: 10.3934/dcdsb.2015.20.1685

2019 Impact Factor: 1.105

Tools

Metrics

  • PDF downloads (62)
  • HTML views (0)
  • Cited by (26)

Other articles
by authors

[Back to Top]

Copyright © 2020 American Institute of Mathematical Sciences