Travelling wave phenomena in non-linear diffusion degenerate Nagumo equations

Journal of Mathematical Biology

Volumn 35, Issue 6, 1997, Pages 713-728

  Sánchez Garduño, Faustino ^b   Maini, Philip K ^a  

^a UNIVERSITY OF OXFORD   (United Kingdom)

^b UNIVERSIDAD NACIONAL AUTÓNOMA DE MÉXICO   (Mexico)

Author keywords

Bifurcation of heteroclinic trajectories; Degenerate diffusion; Hamiltonian; Sharp fronts

Indexed keywords

EID: 0004936581     PISSN: 03036812     EISSN: None     Source Type: Journal    
DOI: 10.1007/s002850050073     Document Type: Article

References (21)

1. Andronov, A. A., Leontovich, E. A., Gordon I. I. and Maier, A. G.: Theory of Dynamic Systems on a Plane (Israel Program for Scientific Translations, Jerusalem, 1973)
2. Aronson D. G. and Weinberger, H. F.: Nonlinear Diffusion in population, genetics and nerve pulse propagation, in Partial Differential Equations and Related Topics, Lecture Notes in Mathematics 446, ed. J.A. Goldstein (Springer Verlag 1975)
3. Aronson, D. G.: Density-Dependent Interaction-Diffusion Systems, in Dynamics and Modelling of Reactive Systems, eds. Steward, W. E., Ray W. H. and Conley C. C. (Academic Press, 1980) 161-176
4. Aronson, D. G.: The role of the diffusion in mathematical population biology: Skellam revisited, in Lecture Notes in Biomathematics 57, eds. V. Capasso, E. Grosso and S.L. Naveri-Fontana (Springer Verlag, 1985)
5. Arrowsmith, D. K. and Place, C. M.: An Introduction to Dynamical Systems (Cambridge University Press, 1990)
6. Carl, E. A.: The Population Control in Arctic Ground Squirrels, Ecology, Vol 52, No. 3, 395-413
7. Carr, J.: Applications of Centre Manifold Theory, (Springer Verlag 1981).
8. Engler, H.: Relations Between Travelling Wave Solutions of Quasilinear Parabolic Equations, Proc. Am. Math. Soc., 93, 297-302 (1985)
9. Gurtin, M. E. and MacCamy, R. C: On the Diffusion of Biological Populations, Math. Biosci., 33, 35-49 (1977)
10. Fisher, R. A.: The Wave of Advance of Advantageous Genes, Ann. Eugenics, 7, 353-367 (1937)
11. Grindrod, P. and Sleeman, B. D.: Weak Travelling Fronts for Population Models with Density-Dependent Dispersion, Math. Meth. in the Appl. Sci., 9, 576-586 (1987)
12. Hadeler, K. P.: Free Boundary Problems in Biology, in Free Boundary Problems: Theory and Applications Vol. II, Eds. A. Fasano and M. Primicerio, (Pitman Advanced Publishing Program, 1983)
13. Hosono, Y.: Travelling Wave Solutions for Some Density Dependent Diffusion Equations, Japan J. Appl. Math., 3, 163-196 (1986)
14. Kappos, E., Hutson, V. C. L. and Michaikow, K.: Conley Index Approach to the Existence of Travelling Wave Solutions for a Scalar Degenerate Reaction-Diffusion Equation (Manuscript 1992)
15. Kolmogoroff, A., Petrovsky, I and Piskounoff, N.: Étude de l'équation de la diffusion evec croissance de la qualité de matiere et son application a un probleme biologique, Moscow Univ. Bull. Math., 1, 1-25 (1937)
16. Murray, J. D.: Mathematical Biology, Biomathematics Texts 19 (Springer Verlag 1989)
17. Myers, J.H. and Krebs, Ch. J.: Population Cycles in Rodents, Sci. Am., 6, 38-46 (1974)
18. Rothe, F.: Asymptotic Behaviour of the Solutions of the Fisher Equation in Lecture Notes in Biomathematics 38, eds. W. Jager, H. Rost and P. Tautu, (Springer-Verlag, 1980)
19. Sánchez-Garduño, F.: Travelling Waves in One-Dimensional Degenerate Non-Linear Reaction-Diffusion Equations, D.Phil, thesis, University of Oxford (1993)
20. Sánchez-Garduño F. and Maini, P. K.: The Existence and Uniqueness of a Sharp Travelling wave Solution for a Generalized Fisher-KPP Equation, J. Math. Biol., 33, 163-192 (1994)
21. Sánchez-Garduño, F. and Maini, P. K.: Travelling Wave Phenomena in some Degenerate Reaction-Diffusion Equations, J. Diff. Eq., 117, 281-319 (1995)