On the Fisher-KPP equation with fast nonlinear diffusion

Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences

Volumn 459, Issue 2038, 2003, Pages 2529-2546

  King, John R ^a   McCabe, Philip M ^a  

^a UNIVERSITY OF NOTTINGHAM   (United Kingdom)

Author keywords

Fast nonlinear diffusion; Population dispersal; Reaction diffusion

Indexed keywords

ARTICLE; DIEL VERTICAL MIGRATION; DIFFUSION; LOGISTIC REGRESSION ANALYSIS; MATHEMATICAL ANALYSIS; NONLINEAR SYSTEM; REACTION ANALYSIS;

EID: 1542616912     PISSN: 13645021     EISSN: 14712946     Source Type: Journal    
DOI: 10.1098/rspa.2003.1134     Document Type: Article

References (15)

1. Budd, C. J. & Collins, G. J. 1997 An invariant moving mesh scheme for the nonlinear diffusion equation. Appl. Numer. Math. 26, 23-39.
2. Engler, H. 1985 Relations between travelling wave solutions to quasilinear parabolic equations. Proc. Am. Math. Soc. 93, 297-302.
3. Fisher, R. A. 1937 The wave of advance of advantageous genes. Ann. Eugenics 7, 355-369.
4. King, J. R. 1993 Self-similar behaviour for the equation of fast nonlinear diffusion. Phil. Trans. R. Soc. Lond. A 343, 337-375.
5. Leach, J. A. & Needham, D. J. 2001 The evolution of reaction-diffusion waves in generalised Fisher equations via matched asymptotic expansions: algebraic corrections. Q. J. Mech. Appl. Math. 54, 157-175.
6. McCabe, P. M., Leach, J. A. & Needham, D. J. 2002 A note on the nonexistence of travelling waves in a class of singular reaction diffusion problems. Dynam. Sys. Int. J. 17, 131-135.
7. MacDonald, D. H. 1997 Hunter-gatherer mating distance and Early Paleoindian social mobility. Curr. Res. Pleistocene 14, 119-121.
8. Murray, J. D. 1989 Mathematical biology. Springer.
9. Needham, D. J. & Barnes, A. N. 1999 Reaction-diffusion and phase waves occurring in a class of scalar reaction-diffusion equations. Nonlinearity 12, 41-58.
10. Newman, W. I. 1980 Some exact solutions to a non-linear diffusion problem in population genetics and combustion. J. Theor. Biol. 85, 325-334.
11. Pablo, A. & Sánchez, A. 1998 Travelling wave behaviour for a Parais-Fisher equation. Eur. J. Appl. Math. 9, 285-304.
12. Rodriguez, A. & Vazquez, J. L. 1990 A well-posed problem in singular Fickian diffusion. Arch. Ration. Mech. Analysis 101, 141-163.
13. Shigesada, N. & Kawasaki, K. 1997 Biological invasions: theory and practice. Oxford University Press.
14. Steele, J., Adams, J. & Sluckin, T. 1998 Modelling Paleoindian dispersals. World Archaeol. 30, 286-305.
15. Young, D. A. & Bettinger, R. L. 1995 Simulating the human expansion in the late Pleistocene. J. Archaeol. Sci. 22, 89-92.