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Third Boundary-Value Problem of the Heat Conduction Equation for a System with Plane-Parallel Boundaries

A. S. Usenko
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Abstract

We obtained a new representation of a solution of the heat conduction equation with boundary condition of the third kind for a layer. The result is presented as a superposition of fundamental solutions for an unbounded system with variable coefficients, the explicit form of which is given. We consider the well-known problem of the evolution of the temperature field initially uniformly distributed in a layer. The distribution of the temperature field is represented in terms of the obtained functions.

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A. S. Usenko. 2001-02-21. Third Boundary-Value Problem of the Heat Conduction Equation for a System with Plane-Parallel Boundaries. https://arxiv.org/abs/math-ph/0102021

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