Hostname: page-component-76fb5796d-r6qrq Total loading time: 0 Render date: 2024-04-26T00:51:20.595Z Has data issue: false hasContentIssue false

On nonlinear processes involving population growth and diffusion

Published online by Cambridge University Press:  14 July 2016

Elliott W. Montroll*
Affiliation:
University of Rochester, N.Y.

Extract

A number of years ago, R. A. Fisher discussed the problem of the propagation of a virile mutant in a population. At about the same time, Kolmogorov, Petrovsky, and Piscounoff, whom we shall refer to as KPP, investigated a general class of partial differential equations which describe simultaneous growth and diffusion processes.

Type
Research Papers
Copyright
Copyright © Sheffield: Applied Probability Trust 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[1] Fisher, R. A. (1937) The wave of advance of advantageous genes. Ann. Eugen. 7, 355369.Google Scholar
[2] Kolmogorov, A., Petrovsky, I. and Piscounov, N. (1937) Etude de l'équation de la diffusion avec croissance de la quantité de matière et son application à un problème biologique. Bull. de l'Univ. d'Etat à Moscou (Sér. Internat.) A, I, 125.Google Scholar
[3] Moran, P.A.P. (1962) The Statistical Processes of Evolutionary Theory. Oxford.Google Scholar
[4] Johnson, W. E. (1963) On a first-order boundary value problem from laminar flame theory. Arch. for Rat. Mech. and Anal. 13, 4654.Google Scholar
[5] Kendall, D. G. (1965) Symposium on Mathematics and Computer Science in Biology and Medicine, London, 213.Google Scholar
[6] Montroll, E. W. and Newell, G. F. (1952) Unsteady-state separation performance of cascades I. J. Appl. Phys. 23, 184194.Google Scholar
[7] Carslaw, H. C. (1943) Introduction to the Mathematical Theory of the Conduction of Heat in Solid Bodies. Dover, New York.Google Scholar