Solution of nonlinear curvature driven evolution of plane convex curves

Solution of nonlinear curvature driven evolution of plane convex curves

The numerical approximation scheme for solving the nonlinear initial value problem ∂tb(v) = ∂xxβ(x, v) + β(x, v) with periodic boundary conditions is presented. Local existence and uniqueness of a solution and convergence of approximations is a consequence of the results of Mikula and Kačur (1996), where the anisotropic curvature driven evolution of plane convex curves is studied. The considere...

Solution of nonlinearly curvature driven evolution of plane curves

The evolution of plane curves obeying the equation v = β(k), where v is normal velocity and k curvature of the curve is studied. Morphological image and shape multiscale analysis of Alvarez, Guichard, Lions and Morel and affine invariant scale space of curves introduced by Sapiro and Tannenbaum as well as isotropic motions of plane phase interfaces studied by Angenent and Gurtin are included in...

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

We study the intrinsic heat equation governing the motion of plane curves. The normal velocity v of the motion is assumed to be a nonlinear function of the curvature and tangential angle of a plane curve Γ. By contrast to the usual approach, the intrinsic heat equation is modified to include an appropriate nontrivial tangential velocity functional α. Short time existence of a regular family of ...

Solution and Application of Anisotropic Curvature Driven Evolution of Curves

Hyperbolic mean curvature flow: Evolution of plane curves

In this paper we investigate the one-dimensional hyperbolic mean curvature flow for closed plane curves. More precisely, we consider a family of closed curves F : S × [0, T ) → R which satisfies the following evolution equation ∂F ∂t (u, t) = k(u, t) ~ N(u, t)− ▽ρ(u, t), ∀ (u, t) ∈ S1 × [0, T ) with the initial data F (u, 0) = F0(u) and ∂F ∂t (u, 0) = f(u) ~ N0, where k is the mean curvature an...