# 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} }

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

#### References

##### Publications referenced by this paper.

SHOWING 1-10 OF 38 REFERENCES

## Metastable patterns in solutions of ut = ϵ2uxx − f(u)

VIEW 4 EXCERPTS

HIGHLY INFLUENTIAL

## Crystal Dislocations with Different Orientations and Collisions

VIEW 4 EXCERPTS

HIGHLY INFLUENTIAL

## Long-time behavior for crystal dislocation

VIEW 4 EXCERPTS

HIGHLY INFLUENTIAL

## Relaxation times for atom dislocations in crystals

VIEW 4 EXCERPTS

HIGHLY INFLUENTIAL

## Strongly Nonlocal Dislocation Dynamics in Crystals

VIEW 4 EXCERPTS

HIGHLY INFLUENTIAL

## $hp$-FEM for the fractional heat equation.

VIEW 2 EXCERPTS