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Exact variational representations for the solution of the simple parabolic equation

Published online by Cambridge University Press:  17 April 2009

R.S. Anderssen
R.S. Anderssen
Affiliation:
Computer Centre, Australian National University, Canberra, ACT.
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Abstract

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By constructing a special set of A-orthonormal functions, it is shown that, under certain smoothness assumptions, the variational and Fourier series representations for the solution of first initial boundary value problems for the simple parabolic differential equation coincide. This result is then extended in order to construct a variational representation for the solution of a very general first initial boundary value problem for this equation.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 5 , Issue 3 , December 1971 , pp. 305 - 314
Copyright
Copyright © Australian Mathematical Society 1971

References

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