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Asymmetric bifurcation

Published online by Cambridge University Press:  17 February 2009

S. Rosenblat
S. Rosenblat
Affiliation:
Department of Mathematics, University of Melbourne, Parkville, Victoria 3052
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Abstract

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A study is made of a non-linear diffusion equation which admits bifurcating solutions in the case where the bifurcation is asymmetric. An analysis of the initial-value problem is made using the method of multiple scales, and the bifurcation and stability characteristics are determined. It is shown that a suitable interpretation of the results can lead to determination of the choice of the bifurcating solution adopted by the system.

Type
Research Article
Information
The ANZIAM Journal , Volume 21 , Issue 3 , January 1980 , pp. 297 - 304
Copyright
Copyright © Australian Mathematical Society 1980

References

[1]Benjamin, T. B., “Bifurcation phenomena in steady flows of a viscous fluid”, Proc. Roy. Soc. A 359 (1978), 1–43.Google Scholar
[2]Davis, S. H. and Segel, L. A., “Effects of surface curvature and property variations on cellular convection’, Phys. Fluids 11 (1968), 470–476.CrossRefGoogle Scholar
[3]Matkowsky, B. J., “A simple nonlinear dynamic stability problem”, Bull. Amer. Math. Soc. 76 (1970), 620–625.CrossRefGoogle Scholar
[4]Segel, L. A. and Stuart, J. T., “On the question of the preferred mode in cellular thermal convection”, J. Fluid Mech. 13 (1962), 289–306.CrossRefGoogle Scholar
[5]Weinberger, H. F. and Rosenblat, S., “The continuous behaviour of bifurcation in the presence of finite noise”, (1980) (to appear).Google Scholar