Invariant imbedding and hyperbolic heat waves

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Abstract
In this paper we build up a general wave splitting and imbedding theory for the solution of both direct and inverse problems associated with thermal processes. It is done by using a full representation of the thermal phenomenon by virtue of Cattaneo’s law. This law by ensuring finite thermal propagation speeds, enables an imbedding equation to be utilised to layer strip the medium; so allowing the solution to the inverse problem of determination of a spatially varying diffusivity. Theoretical results and numerical algorithms are developed and numerical experiments are used to illustrate the effectiveness of the latter.