Spatial decay estimates in transient heat conduction

Authors:
C. O. Horgan, L. E. Payne and L. T. Wheeler

Journal:
Quart. Appl. Math. **42** (1984), 119-127

MSC:
Primary 80A20

DOI:
https://doi.org/10.1090/qam/736512

MathSciNet review:
736512

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Abstract: The spatial decay of solutions to initial-boundary value problems for the heat equation in a three-dimensional cylinder, subject to non-zero boundary conditions only on the ends, is investigated. It is shown that the spatial decay of end effects in the transient problem is *faster* than that for the steady-state case. Qualitative methods involving second-order partial differential inequalities for quadratic functionals are first employed. The explicit spatial decay estimates are then obtained by using comparison principle arguments involving solutions of the *one-dimensional heat equation*. The results give rise to versions of Saint-Venant's principle in transient heat conduction.

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DOI:
https://doi.org/10.1090/qam/736512

Article copyright:
© Copyright 1984
American Mathematical Society