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- W2742445932 abstract "We study the diffusion (or heat) equation on a finite 1-dimensional spatial domain, but we replace one of the boundary conditions with a nonlocal condition, through which we specify a weighted average of the solution over the spatial interval. We provide conditions on the regularity of both the data and weight for the problem to admit a unique solution, and also provide a solution representation in terms of contour integrals. The solution and well-posedness results rely upon an extension of the Fokas (or unified) transform method to initial-nonlocal value problems for linear equations; the necessary extensions are described in detail. Despite arising naturally from the Fokas transform method, the uniqueness argument appears to be novel even for initial-boundary value problems." @default.
- W2742445932 created "2017-08-17" @default.
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- W2742445932 date "2017-08-03" @default.
- W2742445932 modified "2023-09-27" @default.
- W2742445932 title "The diffusion equation with nonlocal data" @default.
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- W2742445932 hasPublicationYear "2017" @default.
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