Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



On a mixed problem for the M`Kendrick-Von Foerster equation

Authors: Akio Yamada and Hiroumi Funakoshi
Journal: Quart. Appl. Math. 40 (1982), 165-192
MSC: Primary 92A05; Secondary 35R30
DOI: https://doi.org/10.1090/qam/666673
MathSciNet review: 666673
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Abstract: A mixed problem for the M'Kendrick-Von Foerster equation is solved explicitly: existence, uniqueness and regularity theorems are proved as well as several integral formulas.

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  • [1] Hiroumi Funakoshi and Akio Yamada, Transition phenomena in bacterial growth between logarithmic and stationary phases, J. Math. Biol. 9 (1980), no. 4, 369–387. MR 661436, https://doi.org/10.1007/BF00276500
  • [2] M. E. Gurtin, A system of equations for age-dependent population diffusion, J. Theor. Biol. 40, 389-392 (1973)
  • [3] Morton E. Gurtin and Richard C. MacCamy, Non-linear age-dependent population dynamics, Arch. Rational Mech. Anal. 54 (1974), 281–300. MR 0354068, https://doi.org/10.1007/BF00250793
  • [4] Edwin Hewitt and Karl Stromberg, Real and abstract analysis, Springer-Verlag, New York-Heidelberg, 1975. A modern treatment of the theory of functions of a real variable; Third printing; Graduate Texts in Mathematics, No. 25. MR 0367121
  • [5] Frank C. Hoppensteadt, Mathematical methods of population biology, Cambridge Studies in Mathematical Biology, vol. 4, Cambridge University Press, Cambridge-New York, 1982. MR 645149
  • [6] Y. Maruyama, T. Komano, H. Fujita, T. Muroyama, T. Ando and T. Ogawa, Synchronization of bacterial cells by glucose starvation, in NRI symposia on modern biology: growth and differentiation in microorganisms, University of Tokyo Press, Tokyo, 1977, 77-93
  • [7] A. G. M'Kendrick, Applications of mathematics to medical problems, Proc. Edinburgh Math. Soc. 44, 98-130 (1926)
  • [8] S. I. Rubinow and R. Oppenheim Berger, Time-dependent solution to age-structured equations for sexual populations, Theoret. Population Biol. 16 (1979), no. 1, 35–47. MR 545479, https://doi.org/10.1016/0040-5809(79)90005-4
  • [9] O. Scherbaum and G. Rasch, Cell size distribution and single cell growth in Tetrahymena pyriformis GL, Acta Pathol. Microbiol. Scand. 41, 161-182 (1957)
  • [10] E. Sinestrari, Non-linear age-dependent population growth, J. Math. Biol. 9, 331-345 (1980)
  • [11] E. Trucco, Mathematical models for cellular systems: the Von Foerster equation. Parts I and II, Bull. Math. Biophys. 27, 285-304, 449-471 (1965)
  • [12] H. Von Foerster, Some remarks on changing populations, in The kinetics of cellular proliferation (F. Stohlman Jr., ed.), Grune and Stratton, New York, 1959, 382-407
  • [13] Akio Yamada and Hiroumi Funakoshi, On von Foerster equation in biomathematics, Mem. Numer. Math. 7 (1980), 29–52. MR 588463

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DOI: https://doi.org/10.1090/qam/666673
Article copyright: © Copyright 1982 American Mathematical Society

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