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Propagation of fronts in a nonlinear fourth order equation

Published online by Cambridge University Press:  01 April 2000

P. LORETI  and
R. MARCH
P. LORETI
Affiliation:
Istituto per le Applicazioni del Calcolo, CNR, Viale del Policlinico 137, 00161 Roma, Italy Current address: Dipartimento Me. Mo. Mat., Universitàd: Roma La Sapienza, Via A. Scarpa 10, 00161 Roma, Italy.
R. MARCH
Affiliation:
Istituto per le Applicazioni del Calcolo, CNR, Viale del Policlinico 137, 00161 Roma, Italy
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Abstract

We consider a geometric motion associated with the minimization of a curvature dependent functional, which is related to the Willmore functional. Such a functional arises in connection with the image segmentation problem in computer vision theory. We show by using formal asymptotics that the geometric motion can be approximated by the evolution of the zero level set of the solution of a nonlinear fourth-order equation related to the Cahn–Hilliard and Allen–Cahn equations.

Type
Research Article
Information
European Journal of Applied Mathematics , Volume 11 , Issue 2 , April 2000 , pp. 203 - 213
Copyright
2000 Cambridge University Press

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