# Uniqueness and existence of spirals moving by forced mean curvature motion

@inproceedings{Forcadel2012UniquenessAE, title={Uniqueness and existence of spirals moving by forced mean curvature motion}, author={N. Forcadel and C. Imbert and R'egis Monneau}, year={2012} }

In this paper, we study the motion of spirals by mean curvature type motion in the (two dimensional) plane. Our motivation comes from dislocation dynamics; in this context, spirals appear when a screw dislocation line reaches the surface of a crystal. The first main result of this paper is a comparison principle for the corresponding parabolic quasi-linear equation. As far as motion of spirals are concerned, the novelty and originality of our setting and results come from the fact that, first… CONTINUE READING

#### Citations

##### Publications citing this paper.

SHOWING 1-5 OF 5 CITATIONS

## Mean curvature flow with driving force on fixed extreme points

VIEW 3 EXCERPTS

CITES BACKGROUND

HIGHLY INFLUENCED

## Steady State and Long Time Convergence of Spirals Moving by Forced Mean Curvature Motion

VIEW 4 EXCERPTS

CITES BACKGROUND

## Verification of one-dimensional models describing anisotropy of step growth

VIEW 2 EXCERPTS

CITES BACKGROUND

## EVOLUTION OF SPIRAL-SHAPED POLYGONAL CURVE BY CRYSTALLINE CURVATURE FLOW WITH A PINNED TIP

VIEW 1 EXCERPT

CITES BACKGROUND

## A non-local free boundary problem arising in a theory of financial bubbles

VIEW 1 EXCERPT

CITES BACKGROUND

#### References

##### Publications referenced by this paper.

SHOWING 1-10 OF 21 REFERENCES

## Spiral solutions for a weakly anisotropic curvature flow equation

VIEW 6 EXCERPTS

HIGHLY INFLUENTIAL

## User’s guide to viscosity solutions of second order partial differential equations

VIEW 8 EXCERPTS

HIGHLY INFLUENTIAL

## Motion of level sets by mean curvature. I

VIEW 4 EXCERPTS

HIGHLY INFLUENTIAL

## Uniqueness and existence of viscosity solutions of generalized mean curvature flow equations

VIEW 5 EXCERPTS

HIGHLY INFLUENTIAL

## A level set method for spiral crystal growth

VIEW 3 EXCERPTS

## Spiral crystal growth

VIEW 1 EXCERPT