Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



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

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