Short time existence for the curve diffusion flow with a contact angle

@inproceedings{Abels2018ShortTE,
  title={Short time existence for the curve diffusion flow with a contact angle},
  author={Helmut Abels and Julia Butz},
  year={2018}
}
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References

SHOWING 1-10 OF 44 REFERENCES
Curve diffusion and straightening flows on parallel lines
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
TLDR
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
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
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...
L 2-flow of elastic curves with clamped boundary conditions
Existence Results for Di usive Surface Motion
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
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
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
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
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
...
...