References
- W. Arendt, A. Grabosch, G. Greiner, U. Groh, H.P. Lotz, U. Moustakas, R. Nagel, F. Neubrander, and U. Schlotterbeck, One-parameter Semigroups of Positive Operators, Springer-Verlag, Berlin, 1986.
- D.M. Auslander, G.F. Oster, and C.B. Huffaker, Dynamics of interacting populations, J. Franklin Inst. 297 (1974), pp. 345–376. doi: 10.1016/0016-0032(74)90039-8
- M. Bai and S. Cui, Analysis of a two-phase cell division model, Appl. Math. Comput. 218 (2012), pp. 4849–4859.
- M. Bai and S. Cui, Well-posedness and asynchronous exponential growth of solutions of a two-phase cell division model, Electron. J. Differ. Equ. 47 (2010), pp. 1–12.
- M. Bai and S. Xu, On a two-phase size-structured population model with infinite states at- birth and distributed delay in birth process, J. Biol. Dyn. 8 (2014), pp. 42–56. doi: 10.1080/17513758.2014.899637
- M. Bai and S. Xu, Global existence of solutions for a nonlinear size-structured population model with distributed delay in the recruitment, Int. J. Math. 26(10) (2015), pp. 1550085-1-20. doi: 10.1142/S0129167X15500858
- J. Banasiak, K. Pichór, and R. Rudnicki, Asynchronous Exponential Growth of a General Structured Population Model, Acta Appl. Math. 119 (2012), pp. 149–166. doi: 10.1007/s10440-011-9666-y
- P. Clément, H. Heijmans, S. Angenent, C. van Duijin, and B. de Pagter, One-parameter Semigroups, Elsevier Science Publishers B.V., North-Holland, Amsterdam, 1987.
- J. Dyson, R. Villella-Bressan, and G.F. Webb, Asynchronous exponential growth in an age structured population of proliferating and quiescent cells, Math. Biosci. 177–178 (2002), pp. 73–83. doi: 10.1016/S0025-5564(01)00097-9
- K.-J. Engel and R. Nagel, One-parameter Semigroups for Linear Evolution Equations, Springer, New York, 2000.
- J.Z. Farkas, Note on asychronous exponential growth for structured population models, Nonlinear Anal TMA 67 (2007), pp. 618–622. doi: 10.1016/j.na.2006.06.016
- J.Z. Farkas and P. Hinow, On a size-structured two-phase population model with infinite states-at-birth, Positivity 14(3) (2010), pp. 501–514. doi: 10.1007/s11117-009-0033-4
- X. Fu, Z. Liu, and P. Magal, Hopf bifurcation in an age-structured population model with two delays, Commun. Pure Appl. Anal. 14 (2015), pp. 657–676. doi: 10.3934/cpaa.2015.14.657
- B. Perthame and L. Ryzhik, Exponential decay for the fragmentation or cell-division equation, J. Differential Equations 210 (2005), pp. 155–177. doi: 10.1016/j.jde.2004.10.018
- S. Piazzera and L. Tonetto, Asynchronous exponential growth for an age dependent population equation with delayed birth process, J. Evol. Eqns. 5 (2005), pp. 61–77. doi: 10.1007/s00028-004-0159-6
- H.R. Thieme, Balanced exponential growth of operator semigroups, J. Math. Anal. Appl. 223 (1998), pp. 30–49. doi: 10.1006/jmaa.1998.5952
- G.B. Zhu and W.L. Chan, A semigroup approach to age dependent population dynamics with time delay, Comm. PDEs 14 (1989), pp. 809–832. doi: 10.1080/03605308908820630