Corpus ID: 219304542

Metastable Speeds in the Fractional Allen-Cahn Equation

@article{Achleitner2020MetastableSI,
  title={Metastable Speeds in the Fractional Allen-Cahn Equation},
  author={Franz Achleitner and Christian Kuehn and Jens Markus Melenk and A. Rieder},
  journal={ArXiv},
  year={2020},
  volume={abs/2006.02731}
}
  • Franz Achleitner, Christian Kuehn, +1 author A. Rieder
  • Published 2020
  • Computer Science, Mathematics
  • ArXiv
  • We study numerically the one-dimensional Allen-Cahn equation with the spectral fractional Laplacian $(-\Delta)^{\alpha/2}$ on intervals with homogeneous Neumann boundary conditions. In particular, we are interested in the speed of sharp interfaces approaching and annihilating each other. This process is known to be exponentially slow in the case of the classical Laplacian. Here we investigate how the width and speed of the interfaces change if we vary the exponent $\alpha$ of the fractional… CONTINUE READING

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