Advances in Differential Equations

On front propagation problems with nonlocal terms

Pierre Cardaliaguet

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We investigate the evolution of compact hypersurfaces of $\mathbb R^N$ depending, not only on terms of curvature of the surface, but also on non local terms such as the measure of the set enclosed by the surface. We present some existence and convexity results for such motions, even for evolutions which do not preserve the inclusion of the initial surfaces.

Article information

Adv. Differential Equations, Volume 5, Number 1-3 (2000), 213-268.

First available in Project Euclid: 27 December 2012

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 53C44: Geometric evolution equations (mean curvature flow, Ricci flow, etc.)
Secondary: 35K55: Nonlinear parabolic equations


Cardaliaguet, Pierre. On front propagation problems with nonlocal terms. Adv. Differential Equations 5 (2000), no. 1-3, 213--268.

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