an:01367740
Zbl 0938.65145
Mikula, Karol; ??ev??ovi??, Daniel
Solution of nonlinearly curvature driven evolution of plane curves
EN
Appl. Numer. Math. 31, No. 2, 191-207 (1999).
00060053
1999
j
65P10 37C10 65M20 35K05
curve evolution; image and shape multiscale analysis; phase interface; nonlinear degenerate parabolic equations; numerical experiments
Authors' abstract: The evolution of plane curves obeying the equation \(v=\beta(k)\), where \(v\) is normal velocity and \(k\) curvature of the curve is studied. Morphological image and shape multiscale analysis of \textit{L. Alvarez}, \textit{F. Guichard}, \textit{P.-L. Lions} and \textit{J.-M. Morel} [Axioms and fundamental equations of image processing, Arch. Ration. Mech. Anal. 123, No. 3, 199-257 (1993; Zbl 0788.68153)] and affine invariant scale space of curves introduced by \textit{G. Sapiro} and \textit{A. Tannenbaum} [J. Funct. Anal. 119, No. 1, 79-120 (1994; Zbl 0801.53008)] as well as isotropic motions of plane phase interfaces studied by \textit{S. B. Angenent} and \textit{M. E. Gurtin} [Multiphase thermomechanics with an interfacial structure. II: Evolution of an isothermal interface, Arch. Rat. Mech. Anal. 108, 323-391 (1989); J. Reine Angew. Math. 446, 1-47 (1994; Zbl 0784.35124)] are included in the model. We introduce and analyze a numerical scheme for solving the governing equation and present numerical experiments.
R.Gorenflo (Berlin)
Zbl 0788.68153; Zbl 0801.53008; Zbl 0784.35124