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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.

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