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Solution of nonlinearly curvature driven evolution of plane curves. (English) Zbl 0938.65145
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 L. Alvarez, F. Guichard, P.-L. Lions and 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 G. Sapiro and 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 S. B. Angenent and 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.

65P10 Numerical methods for Hamiltonian systems including symplectic integrators
37C10 Dynamics induced by flows and semiflows
65M20 Method of lines for initial value and initial-boundary value problems involving PDEs
35K05 Heat equation
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