Dual extremum principles relating to cooling fins

Authors:
S. Bhargava and R. J. Duffin

Journal:
Quart. Appl. Math. **31** (1973), 27-41

MSC:
Primary 80.49

DOI:
https://doi.org/10.1090/qam/416294

MathSciNet review:
416294

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Abstract: Under consideration is a differential equation of the Sturm--Liouville type where the function is given. The problem is to find a function in , a constant and a solution of the corresponding differential equation such that the energy functional is maximized when is subject to the constraint and is subject to the boundary conditions at and at . Here and are constants. A key relation , where is a positive constant, is found. This criterion leads to explicit solution of the problem. A further consequence of this criterion together with a pair of dual extremum principles is a ``duality inequality'' giving sharp upper and lower estimates of the maximum value of the energy functional.

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DOI:
https://doi.org/10.1090/qam/416294

Article copyright:
© Copyright 1973
American Mathematical Society