Source identification for the heat equation. (English) Zbl 0696.35187

Summary: The problem of determining an unknown heat source in a homogeneous, semi- infinite slab from measured temperature and flux data is examined. When the source is separable into a product of temporal and spatial components, a functional relationship is derived that relates the Laplace transforms of these components. Examples considered include a point source with oscillating intensity and a spatial layer undergoing exponential decay. A source of non-separable type in the form of a moving front is also treated.


35R30 Inverse problems for PDEs
35K05 Heat equation
44A10 Laplace transform
80A20 Heat and mass transfer, heat flow (MSC2010)
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[1] Laventiev, M. M.; Romanov, V. G.; Vasiliev, I., Multidimensional Inverse Problems for Differential Equations, Lecture Notes in Mathematics, 167 (1970), Springer-Verlag: Springer-Verlag New York · Zbl 0208.36403
[2] Beck, J. V.; Blackwell, B.; Clair, C. B.St., Inverse Heat Conduction (1985), Wiley: Wiley New York · Zbl 0633.73120
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