## 5 Citations

On the Surface Diffusion Flow with Triple Junctions in Higher Space Dimensions

- MathematicsGeometric Flows
- 2020

Abstract We show short time existence for the evolution of triple junction clusters driven by the surface diffusion flow. On the triple line we use the boundary conditions derived by Garcke and…

A Blow-up Criterion for the Curve Diffusion Flow with a Contact Angle

- MathematicsSIAM J. Math. Anal.
- 2020

We prove a blow-up criterion in terms of an $L_2$-bound of the curvature for solutions to the curve diffusion flow if the maximal time of existence is finite. In our setting, we consider an evolvin...

A Survey of the Elastic Flow of Curves and Networks

- MathematicsMilan Journal of Mathematics
- 2021

We collect and present in a unified way several results in recent years about the elastic flow of curves and networks, trying to draw the state of the art of the subject. In particular, we give a…

Global solution and global orbit to reaction–diffusion equation for fractional Dirichlet‐to‐Neumann operator with subcritical exponent

- MathematicsMathematical Methods in the Applied Sciences
- 2020

We consider the reaction–diffusion equation for fractional Dirichlet‐to‐Neumann operator with subcritical exponent motivated by electrical impedance tomography (EIT) and a need to overcome the…

## References

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Curve diffusion and straightening flows on parallel lines

- Mathematics
- 2017

In this paper, we study families of immersed curves $\gamma:(-1,1)\times[0,T)\rightarrow\mathbb{R}^2$ with free boundary supported on parallel lines $\{\eta_1,…

Evolution of Elastic Curves in Rn: Existence and Computation

- MathematicsSIAM J. Math. Anal.
- 2002

Long-time existence is proved in the two cases when a multiple of length is added to the energy or the length is fixed as a constraint, and a lower bound for the lifespan of solutions to the curve diffusion flow is observed.

Curvature Driven Interface Evolution

- Mathematics
- 2013

Curvature driven surface evolution plays an important role in geometry, applied mathematics and in the natural sciences. In this paper geometric evolution equations such as mean curvature flow and…

A Blow-up Criterion for the Curve Diffusion Flow with a Contact Angle

- MathematicsSIAM J. Math. Anal.
- 2020

We prove a blow-up criterion in terms of an $L_2$-bound of the curvature for solutions to the curve diffusion flow if the maximal time of existence is finite. In our setting, we consider an evolvin...

Existence Results for Di usive Surface Motion

- Mathematics
- 1997

Three geometric interface laws for the evolution of curves are considered. They include the motion by surface diiusion and the conserved mean curvature ow. All these laws decrease length and preserve…

A singular limit for a system of degenerate Cahn-Hilliard equations

- Mathematics
- 2000

A singular limit is considered for a system of Cahn-Hilliard equations with a degenerate mobility matrix near the deep quench limit. Via formal asymptotics, this singular limit is seen to give rise…

Willmore-Helfrich L^{2}-flow of curves with natural boundary conditions

- Mathematics
- 2012

We consider regular open curves in R^n with fixed boundary points and moving according to the L^{2}-gradient flow for a generalisation of the Helfrich functional. Natural boundary conditions are…

Evolution of open elastic curves in ℝn subject to fixed length and natural boundary conditions

- Mathematics
- 2014

Abstract We consider regular open curves in ℝn with fixed boundary points, curvature equal to zero at the boundary, subject to a fixed length constraint and moving according to the L2-gradient flow…

The Cahn–Hilliard equation with a concentration dependent mobility: motion by minus the Laplacian of the mean curvature

- MathematicsEuropean Journal of Applied Mathematics
- 1996

We show by using formal asymptotics that the zero level set of the solution to the Cahn–Hilliard equation with a concentration dependent mobility approximates to lowest order in ɛ. an interface…