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On transformations of the biharmonic equation

  • George W. Bluman (a1) and R. Douglas Gregory (a2)

Abstract

Consider a point transformation of the biharmonic equation

namely a coordinate transformation

together with a change of dependent variable given by

for some multiplier F(ξ, η).

Copyright

References

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4.Bluman, G. and Cole, J. D.. Similarity Methods for Differential Equations (Springer, New York, Heidelberg, Berlin, 1974).
5.Jeffery, G. B.. Plane stress and plane strain in bipolar coordinates. Phil. Trans. Roy. Soc. A, 221 (1921), 265293.
6.Lie, S.. Über die Integration durch bestimmte Integrale von einer Klasse linearer partieller Differentialgleichungen. Arch. Math. Naturvidensk, 6 (1881), 328368.
7.Michell, J. H.. The inversion of plane stress. Proc. Lond. Math. Soc, 34 (1901), 134142.
8.Ovsiannikov, L. V.. Group Analysis of Differential Equations (Academic Press, New York, 1982).
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10.Ahlbrandt, C. D., Hinton, D. B. and Lewis, R. T.. Inversion in the unit sphere for powers of the Laplacian. Ordinary Differential Equations and Operators. Lecture Notes in Mathematics, 1032 (Springer, 1983), 18.
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