A Class of Parabolic Equations Driven by the Mean Curvature Flow

A Class of Parabolic Equations Driven by the Mean Curvature Flow

We study a class of parabolic equations which can be viewed as a generalized mean curvature flow acting on cylindrically symmetric surfaces with a Dirichlet condition on the boundary. We prove the existence of a unique solution by means of an approximation scheme. We also develop the theory of asymp...

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Veröffentlicht in:Proceedings of the Edinburgh Mathematical Society 2019-02, Vol.62 (1), p.135-163
Hauptverfasser: de Araujo, Anderson L. A., Montenegro, Marcelo
Format: Artikel
Sprache:eng
Schlagworte:
Curvature
Dirichlet problem
Mathematical analysis
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Beschreibung
Zusammenfassung:We study a class of parabolic equations which can be viewed as a generalized mean curvature flow acting on cylindrically symmetric surfaces with a Dirichlet condition on the boundary. We prove the existence of a unique solution by means of an approximation scheme. We also develop the theory of asymptotic stability for solutions of general parabolic problems.
ISSN:0013-0915
1464-3839
DOI:10.1017/S001309151800038X