zbMATH — the first resource for mathematics

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)
Full Text: DOI
[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
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.