Abstract
We show short-time existence for curves driven by curve diffusion flow with a prescribed contact angle alpha is an element of (0, pi): The evolving curve has free boundary points, which are supported on a line and it satisfies a no-flux condition. The initial data are suitable curves of class W-2(gamma) with gamma is an element of (3/2, 2]. For the proof the evolving curve is represented by a ...
Abstract
We show short-time existence for curves driven by curve diffusion flow with a prescribed contact angle alpha is an element of (0, pi): The evolving curve has free boundary points, which are supported on a line and it satisfies a no-flux condition. The initial data are suitable curves of class W-2(gamma) with gamma is an element of (3/2, 2]. For the proof the evolving curve is represented by a height function over a reference curve: The local well-posedness of the resulting quasilinear, parabolic, fourth-order PDE for the height function is proven with the help of contraction mapping principle. Difficulties arise due to the low regularity of the initial curve. To this end, we have to establish suitable product estimates in time weighted anisotropic L-2-Sobolev spaces of low regularity for proving that the non-linearities are well-defined and contractive for small times. (C) 2019 Elsevier Inc. All rights reserved.
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