Abstract
In this paper, we develop a global domain-boundary integral theory for the one-dimensional heat equation with an unknown space–time dependent heat source. A generalized Green’s second identity is derived for a global relation of the unknown heat source under boundary conditions on the whole space–time boundary. Accordingly, we can develop a numerical algorithm based on the global method, which is effective for the inverse heat source problem (IHSP). The global boundary integral equation method (GBIEM) can retrieve the unknown heat source by merely needing the boundary measurements of data, including a final time condition. Several numerical examples of the IHSP demonstrate that the present method is effective and stable, even for those of strongly ill-posed ones under quite large noises.
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