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- W4289382616 abstract "We prove a blow-up criterion in terms of an $L_2$-bound of the curvature for solutions to the curve diffusion flow if the maximal time of existence is finite. In our setting, we consider an evolving family of curves driven by curve diffusion flow, which has free boundary points supported on a line. The evolving curve has fixed contact angle $alpha in (0, pi)$ with that line and satisfies a no-flux condition. The proof is led by contradiction: A compactness argument combined with the short time existence result enables us to extend the flow, which contradicts the maximality of the solution." @default.
- W4289382616 created "2022-08-02" @default.
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- W4289382616 date "2018-10-16" @default.
- W4289382616 modified "2023-09-28" @default.
- W4289382616 title "A Blow-up Criterion for the Curve Diffusion Flow with a Contact Angle" @default.
- W4289382616 doi "https://doi.org/10.48550/arxiv.1810.07257" @default.
- W4289382616 hasPublicationYear "2018" @default.
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