Evolution of Plane Curves Driven by a Nonlinear Function of Curvature and Anisotropy

@article{Sevcovic2001EvolutionOP,
  title={Evolution of Plane Curves Driven by a Nonlinear Function of Curvature and Anisotropy},
  author={Daniel Sevcovic and Karol Mikula},
  journal={SIAM Journal of Applied Mathematics},
  year={2001},
  volume={61},
  pages={1473-1501}
}
In this paper we study evolution of plane curves satisfying a geometric equation v = β(k, ν), where v is the normal velocity and k and ν are the curvature and tangential angle of a plane curve Γ. We follow the direct approach and we analyze the so-called intrinsic heat equation governing the motion of plane curves obeying such a geometric equation. The intrinsic heat equation is modified to include an appropriate nontrivial tangential velocity functional α. We show how the presence of a… CONTINUE READING