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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    References

    Publications referenced by this paper.
    SHOWING 1-10 OF 28 REFERENCES
    Nonlocal and multipoint boundary value problems for linear evolution equations
    3
    Two-point boundary value problems for linear evolution equations
    38
    The Linear KdV Equation with an Interface
    16
    A Unified Approach To Boundary Value Problems
    264
    Interface Problems for Dispersive Equations
    20
    Well-posed two-point initial-boundary value problems with arbitrary boundary conditions
    25