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On Certain Types of Solution of the Equation of Heat Conduction
Published online by Cambridge University Press: 18 May 2009
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Let f(x, y, z, t) satisfy the equation
For certain purposes, particularly in connection with the propagation of a boundary of fusion etc., it is of interest to discover solutions of (1) which permit the equation:
to be solved explicitly in the form:
This suggests the examination of solutions of the type
where
and f, ϕ, ψ are functions to be determined. To save repetition, Roman capitals denote arbitrary constants throughout.
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- Copyright © Glasgow Mathematical Journal Trust 1952
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