Summary
A mathematical model describing the dynamics of a population consisting of several species is studied. The interactions in the population are assumed to be age-specific. Using an evolution equation approach, sufficient conditions for well-posedness in L 1 of the dynamics and for existence as well as for stability of equilibrium solutions are given.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Di Blasio, G.: Nonlinear age-dependent population diffusion. J. Math. Biol. 8, 265–284 (1979)
Coffman, C. V., Coleman, B. D.: On the growth of populations with narrow spread in reproductive age I, II, III. J. Math. Biol. 6, 1–19; 6, 285–303 (1978); 7, 281–301 (1979)
Daher, J.: On a fixed point principle of Sadovskii. Nonlin. Anal. 2, 643–645 (1978)
Daleckii, J. L., Krein, M. G.: Stability of solutions of differential equations in Banach spaces. Transl. Math. Monographs, Vol. 43. Providence, Rhode Island: AMS 1974
von Foerster, H.: Some remarks on changing populations. In: The kinetics of cellular proliferation, pp. 382–407. New York: Grune and Stratton 1959
Gurtin, M. E.: A system of equations for age-dependent population diffusion. J. Theoret. Biol. 40, 389–392 (1973)
Gurtin, M. E., MacCamy, R. C.: Nonlinear age-dependent population dynamics. Arch. Rational Mech. Anal. 54, 281–300 (1974)
Hille, E., Phillips, R. S.: Functional analysis and semigroups. AMS Colloq. Publ. Vol. 31. Providence, Rhode Island 1957
Martin, R. H.: Nonlinear operators and differential equations in Banach spaces. New York: John Wiley 1976
Mönch, H., von Harten, G.: On the Cauchy problem for ordinary differential equations in Banach spaces. Arch. Math., in press (1980)
Prüß, J.: Semilineare Integrodifferentialgleichungen. Dissertation, Paderborn 1978
Prüß, J.: Periodic solutions of semilinear evolution equations. Nonlin. Anal. 3, 601–612 (1979)
Rotenberg, M.: Equilibrium and stability in populations whose interactions are age-specific. J. Theoret. Biol. 54, 207–224 (1975)
Sowunmi, C. O. A.: Female dominant age-dependent deterministic population dynamics. J. Math. Biol. 3, 9–17(1976)
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Prüß, J. Equilibrium solutions of age-specific population dynamics of several species. J. Math. Biology 11, 65–84 (1981). https://doi.org/10.1007/BF00275825
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF00275825