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, +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

#### References

##### Publications referenced by this paper.
SHOWING 1-10 OF 38 REFERENCES

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

• Mathematics
• 1989
VIEW 4 EXCERPTS
HIGHLY INFLUENTIAL

## Crystal Dislocations with Different Orientations and Collisions

• Mathematics, Physics
• 2014
VIEW 4 EXCERPTS
HIGHLY INFLUENTIAL

## Long-time behavior for crystal dislocation

• Stefania Patrizi, Enrico Valdinoci
• dynamics. Math. Models Methods Appl. Sci.,
• 2017
VIEW 4 EXCERPTS
HIGHLY INFLUENTIAL

## Relaxation times for atom dislocations in crystals

• Physics, Mathematics
• 2015
VIEW 4 EXCERPTS
HIGHLY INFLUENTIAL

## Strongly Nonlocal Dislocation Dynamics in Crystals

• Mathematics, Physics
• 2013
VIEW 4 EXCERPTS
HIGHLY INFLUENTIAL

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

• Mathematics
• 2019
VIEW 2 EXCERPTS

## A Crank-Nicolson ADI Spectral Method for a Two-Dimensional Riesz Space Fractional Nonlinear Reaction-Diffusion Equation

VIEW 1 EXCERPT

## A PDE Approach to Space-Time Fractional Parabolic Problems

• Mathematics, Computer Science
• SIAM J. Numer. Anal.
• 2016
VIEW 1 EXCERPT

## A fast Galerkin finite element method for a space-time fractional Allen-Cahn equation

• Mathematics, Computer Science
• J. Comput. Appl. Math.
• 2020
VIEW 1 EXCERPT

## A fractional phase-field model for two-phase flows with tunable sharpness: Algorithms and simulations

• Mathematics
• 2016
VIEW 1 EXCERPT