Closed Hypersurfaces Driven by Mean Curvature and Inner Pressure
Thilo Notz
Source abstract
Abstract We introduce a hyperbolic equation that describes the motion of closed hypersurfaces in a Riemannian manifold with surface tension and inner pressure as driving forces. In the case of spherical surfaces this equation can be considered as an idealized mathematical model for a moving soap bubble. The equation is derived as an Euler‐Lagrange equation from a suitable action integral. It is a quasi‐linear degenerate hyperbolic PDE of second order that describes the motion of the surfaces extrinsically. Our main results are the solution of the Cauchy problem by means of the Nash‐Moser inverse function theorem, a continuation criterion, and stability estimates. © 2012 Wiley Periodicals, Inc.
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