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.
- 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, DOI https://doi.org/10.1007/BF00276500
M. E. Gurtin, A system of equations for age-dependent population diffusion, J. Theor. Biol. 40, 389–392 (1973)
- Morton E. Gurtin and Richard C. MacCamy, Non-linear age-dependent population dynamics, Arch. Rational Mech. Anal. 54 (1974), 281–300. MR 354068, DOI https://doi.org/10.1007/BF00250793
- 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
- Frank C. Hoppensteadt, Mathematical methods of population biology, Cambridge Studies in Mathematical Biology, vol. 4, Cambridge University Press, Cambridge-New York, 1982. MR 645149
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
A. G. M’Kendrick, Applications of mathematics to medical problems, Proc. Edinburgh Math. Soc. 44, 98–130 (1926)
- 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, DOI https://doi.org/10.1016/0040-5809%2879%2990005-4
O. Scherbaum and G. Rasch, Cell size distribution and single cell growth in Tetrahymena pyriformis GL, Acta Pathol. Microbiol. Scand. 41, 161–182 (1957)
E. Sinestrari, Non-linear age-dependent population growth, J. Math. Biol. 9, 331–345 (1980)
E. Trucco, Mathematical models for cellular systems: the Von Foerster equation. Parts I and II, Bull. Math. Biophys. 27, 285–304, 449–471 (1965)
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
- Akio Yamada and Hiroumi Funakoshi, On von Foerster equation in biomathematics, Mem. Numer. Math. 7 (1980), 29–52. MR 588463
H. Funakoshi and A. Yamada, Transition phenomena in bacterial growth between logarithmic and stationary phases, J. Math. Biol. 9, 369–387 (1980)
M. E. Gurtin, A system of equations for age-dependent population diffusion, J. Theor. Biol. 40, 389–392 (1973)
M. E. Gurtin and R. C. MacCamy, Non-linear age-dependent population dynamics, Arch. Rational Mech. Anal. 54, 281–300 (1974)
E. Hewitt and K. Stromberg, Real and abstract analysis, Springer, Berlin, 1965
F. C. Hoppensteadt, Mathematical methods of population biology, Courant Institute of Mathematical Sciences: New York University, New York, 1976
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
A. G. M’Kendrick, Applications of mathematics to medical problems, Proc. Edinburgh Math. Soc. 44, 98–130 (1926)
S. I. Rubinow, Time-dependent solution to age-structured equations for sexual populations, Theor. Pop. Biol. 16, 35–47 (1979)
O. Scherbaum and G. Rasch, Cell size distribution and single cell growth in Tetrahymena pyriformis GL, Acta Pathol. Microbiol. Scand. 41, 161–182 (1957)
E. Sinestrari, Non-linear age-dependent population growth, J. Math. Biol. 9, 331–345 (1980)
E. Trucco, Mathematical models for cellular systems: the Von Foerster equation. Parts I and II, Bull. Math. Biophys. 27, 285–304, 449–471 (1965)
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
A. Yamada and H. Funakoshi, On Von Foerster equation in biomathematics, Memoirs of Numerical Math. 7, 29–52 (1980)
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Article copyright:
© Copyright 1982
American Mathematical Society
