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Exact variational representations for the solution of the simple parabolic equation
Published online by Cambridge University Press: 17 April 2009
Abstract
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