×

On the age-dependent population dynamics with delayed dependence of the structure. (English) Zbl 1239.35163

Summary: The paper deals with the description of the a model of the population with delayed dependence of the structure. We present the proof of the existence and the uniqueness of the solution of this problem.

MSC:

35Q92 PDEs in connection with biology, chemistry and other natural sciences
92D25 Population dynamics (general)
35A01 Existence problems for PDEs: global existence, local existence, non-existence
35A02 Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] McKendrick, A. G., Application of mathematics to medical problems, Proc. Edinb. Math. Soc., 44, 98-130 (1926) · JFM 52.0542.04
[2] Gurtin, M. E.; MacCamy, R. C., Non-linear age-dependent population dynamics, Arch. Ration. Mech. Anal., 54, 281-300 (1974) · Zbl 0286.92005
[3] Busoni, G.; Palczewski, A., Dynamics of a two sex population with gestation period, Appl. Math. (Warsaw), 27, 1, 21-34 (2000) · Zbl 0990.92031
[4] M. Wa zewska-Czy zewska, A. Lasota, Matematyczne problemy dynamiki układu krwinek czerwonych, Roczniki PTM, Matematyka Stosowana, (1976), VI, 23-40; M. Wa zewska-Czy zewska, A. Lasota, Matematyczne problemy dynamiki układu krwinek czerwonych, Roczniki PTM, Matematyka Stosowana, (1976), VI, 23-40
[5] Marchuk, G. I., Mathematical Models in Immunology (1983), Springer: Springer New York · Zbl 0825.92076
[6] Foryś, U., Biological delay systems and the Mikhailov criterion of stability, J. Biol. Syst., 12, 1, 1-16 (2001)
[7] Leszczyński, H.; Zwierkowski, P., Existence of solutions to generalized von Foerster equations with functional dependence, Ann. Polon. Math., 83, 3, 201-210 (2004) · Zbl 1109.35118
[8] Łoskot, K., Bounded solutions of a system of partial differential equations describing interacting cell populations, Bull. Polish Acad. Sci. Math., 42, 4, 315-343 (1994) · Zbl 0826.35130
[9] Haribash, N., Delayed von Foerster equation, Univ. Iagel. Acta Math., 39, 239-248 (2001) · Zbl 1001.35120
[10] Forystek, E., On the system of nonlinear von Foerster equations, Univ. Iagel. Acta Math., 38, 199-204 (2000) · Zbl 1012.35084
[11] Bielecki, A., Une remarque sur la méthode de Banach - Caciopoli - Tikhonov dans la théorie des équations différentielles ordinaires, Bull. Acad. Pol. Sci., 4, 261-268 (1956) · Zbl 0070.08103
[12] Arino, O.; Hbid, M. L.; Ait Dads, E., Delay Differential Equations and Applications (2006), Springer: Springer Dordrecht · Zbl 1116.34002
[13] A.L. Dawidowicz, A. Poskrobko, Age-dependent population dynamics with the delayed argument, Progress in Nonlinear Differential Equations and their Applications, vol. 75, pp. 165-174; A.L. Dawidowicz, A. Poskrobko, Age-dependent population dynamics with the delayed argument, Progress in Nonlinear Differential Equations and their Applications, vol. 75, pp. 165-174 · Zbl 1207.35094
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.