Linear evolution equations on the half-line with dynamic boundary conditions

@article{Smith2019LinearEE,
  title={Linear evolution equations on the half-line with dynamic boundary conditions},
  author={D. A. Smith and Wei Yan Toh},
  journal={arXiv: Analysis of PDEs},
  year={2019}
}
The classical half line Robin problem for the heat equation may be solved via a spatial Fourier transform method. In this work, we study the problem in which the static Robin condition $bq(0,t)+q_x(0,t)=0$ is replaced with a dynamic Robin condition; $b=b(t)$ is allowed to vary in time. We present a solution representation, and justify its validity, via an extension of the Fokas transform method. We show how to reduce the problem to a variable coefficient fractional linear ordinary differential… 

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