7 citations · 13 across the 10 of their papers we have counts for
18 papers
Convergence of solutions to a convective Cahn-Hilliard type equation of the sixth order in case of small deposition rates
Piotr Rybka, Glen Wheeler
We show stabilisation of solutions to the sixth-order convective Cahn-Hilliard equation. {The problem} has the structure of a gradient flow perturbed by a quadratic destabilising t…
The -elastic flow for planar closed curves with constant parametrization
Shinya Okabe, Glen Wheeler
In this paper, we consider the -gradient flow for the modified -elastic energy defined on planar closed curves. We formulate a notion of weak solution for the flow and prov…
On the -gradient flow for the length functional
Philip Schrader, Glen Wheeler, Valentina-Mira Wheeler
In this article we consider the length functional defined on the space of immersed planar curves. The Riemannian metric gives rise to the curve shortening flow as the gra…
The length-constrained ideal curve flow
James McCoy, Glen Wheeler, Yuhan Wu
A recent article by the first two authors together with B Andrews and V-M Wheeler considered the so-called `ideal curve flow', a sixth order curvature flow that seeks to deform clo…
Convergence for global curve diffusion flows
Glen Wheeler
In this note we establish exponentially fast smooth convergence for global curve diffusion flows, and discuss open problems relating embeddedness to global existence (Giga's conjec…
Theory and numerics for Chen's flow of curves
Matthew Cooper, Glen Wheeler, Valentina-Mira Wheeler
In this article we study Chen's flow of curves from theoreical and numerical perspectives. We investigate two settings: that of closed immersed -circles, and immersed lines sati…