Interior Value Problems of Mathematical Physics. Part II. Heat Conduction

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Abstract
In contrast to the solution of Interior and Boundary Value Problems (IVP and BVP) in wave propagation, it is not possible to provide the simplifications made available by the Heaviside wave-expansion technique for heat conduction. The application of the Laplace transform to IVP in heat conduction generally involves the explicit application of the inversion theorem— contour integration and the evaluation of residues at poles in the complex plane. Following the presentation of solutions to some representative IVP in heat conduction in slab, cylindrical, and spherical geometry, it is shown how a heat-conduction problem in the semi-infinite domain may be reduced to a case for the finite domain. The need for the application of integral equation techniques is thus avoided. A discussion of the connection between the IVP and BVP is presented on the subject of potential theory and the phenomenon of vision as an IVP in optics.

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