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Zbl 0712.49039
Visintin, Augusto
Pattern evolution. (English)
[J] Ann. Sc. Norm. Super. Pisa, Cl. Sci., IV. Ser. 17, No.2, 197-225 (1990). ISSN 0391-173X

A variational model of the evolution of Euclidean sets is proposed. In particular it includes the evolution of sets either of finite perimeter or with boundary of fractional dimension. This model of morphogenesis is based on the introduction of a discontinuous hysteresis effect in time; it consists of a system of two variational inequalities coupled with a nonconvex constraint. The existence of a solution is proven by means of approximation by time discretization, a priori estimates and passage to the limit. Applications to the study of two-phase systems with surface tension, and to pattern interpolation are also discussed.
[A.Visintin]

MSC 2000:: *49Q05 Minimal surfaces (calculus of variations)
49J40 Variational methods including variational inequalities

Keywords: generalized coarea formula; boundary of fractional dimension; morphogenesis; hysteresis; two-phase systems; surface tension; pattern interpolation

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