Stability and regularity results for a size-structured population model

Journal of Mathematical Analysis and Applications

Volumn 328, Issue 1, 2007, Pages 119-136

  Farkas, Jozsef Z ^a   Hagen, Thomas ^a  

^a University of Memphis   (United States)

Author keywords

Population dynamics; Size structured; Spectral analysis; Stability theory

Indexed keywords

EID: 33845863686     PISSN: 0022247X     EISSN: 10960813     Source Type: Journal    
DOI: 10.1016/j.jmaa.2006.05.032     Document Type: Article

References (25)

1. Ackleh A.S., Deng K., and Hu S. A quasilinear hierarchical size-structured model: Well-posedness and approximation. Appl. Math. Optim. 51 (2005) 35-59
2. Calsina A., and Saldaña J. A model of physiologically structured population dynamics with a nonlinear individual growth rate. J. Math. Biol. 33 (1995) 335-364
3. Calsina A., and Saldaña J. Asymptotic behaviour of a model of hierarchically structured population dynamics. J. Math. Biol. 35 (1997) 967-987
4. Calsina A., and Sanchón M. Stability and instability of equilibria of an equation of size structured population dynamics. J. Math. Anal. Appl. 286 (2003) 435-452
5. O. Diekmann, M. Gyllenberg, J.A.J. Metz, Physiologically structured population models: Towards a general mathematical theory, in: Y. Takeuchi, Y. Iwasa, K. Sato (Eds.), Mathematics for Ecology and Environmental Sciences, Springer, New York, in press
6. Diekmann O., Gyllenberg M., Metz J.A.J., and Thieme H.R. On the formulation and analysis of general deterministic structured population models: I. Linear theory. J. Math. Biol. 36 (1998) 349-388
7. Diekmann O., Gyllenberg M., Huang H., Kirkilionis M., Metz J.A.J., and Thieme H.R. On the formulation and analysis of general deterministic structured population models: II. Nonlinear theory. J. Math. Biol. 43 (1998) 157-189
8. Engel K.-J., and Nagel R. One-Parameter Semigroups for Linear Evolution Equations (2000), Springer, New York
9. Farkas J.Z. Stability conditions for the nonlinear McKendrick equations. Appl. Math. Comput. 156 (2004) 771-777
10. Farkas J.Z. Stability conditions for a nonlinear size-structured model. Nonlinear Anal. Real World Appl. 6 (2005) 962-969
11. Farkas M. On the stability of stationary age distributions. Appl. Math. Comput. 131 (2002) 107-123
12. Greiner G. Perturbing the boundary conditions of a generator. Houston J. Math. 13 (1987) 213-229
13. Gurtin M.E., and MacCamy R.C. Nonlinear age-dependent population dynamics. Arch. Ration. Mech. Anal. 54 (1974) 281-300
14. Hagen T. Eigenvalue asymptotics in isothermal forced elongation. J. Math. Anal. Appl. 244 (2000) 393-407
15. Hagen T. On the semigroup of linearized forced elongation. Appl. Math. Lett. 18 (2005) 667-672
16. Hagen T. Asymptotic solutions of characteristic equations. Nonlinear Anal. Real World Appl. 6 (2005) 429-446
17. Hagen T. Linear theory of nonisothermal forced elongation. J. Evol. Equ. 5 (2005) 417-440
18. Hagen T., and Renardy M. Eigenvalue asymptotics in nonisothermal elongational flow. J. Math. Anal. Appl. 252 (2000) 431-443
19. Hagen T., and Renardy M. Studies on the linear equations of melt-spinning of viscous fluids. Differential Integral Equations 14 (2001) 19-36
20. Iannelli M. Mathematical Theory of Age-Structured Population Dynamics (1994), Giardini Editori, Pisa
21. Kato N. A principle of linearized stability for nonlinear evolution equations. Trans. Amer. Math. Soc. 347 (1995) 2851-2868
22. Metz J.A.J., and Diekmann O. The Dynamics of Physiologically Structured Populations (1986), Springer, Berlin
23. Pazy A. Semigroups of Linear Operators and Applications to Partial Differential Equations (1983), Springer, New York
24. Prüß J. Stability analysis for equilibria in age-specific population dynamics. Nonlinear Anal. 7 (1983) 1291-1313
25. Webb G. Theory of Nonlinear Age-Dependent Population Dynamics (1985), Marcel Dekker, New York