The diffusion equation with nonlocal data

P. Miller; D. Smith

DOI:10.1016/J.JMAA.2018.05.064

Corpus ID: 119158503

The diffusion equation with nonlocal data

@article{Miller2017TheDE,
  title={The diffusion equation with nonlocal data},
  author={P. Miller and D. Smith},
  journal={arXiv: Analysis of PDEs},
  year={2017}
}

P. Miller, D. Smith

Published 2017

Mathematics

arXiv: Analysis of PDEs

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… CONTINUE READING

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