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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:
35R30Inverse problems for PDE
35K05Heat equation
44A10Laplace transform
80A20Heat and mass transfer, heat flow