Abels, Helmut and Butz, Julia (2020) A BLOW-UP CRITERION FOR THE CURVE DIFFUSION FLOW WITH A CONTACT ANGLE. SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 52 (3). pp. 2592-2623. ISSN 0036-1410, 1095-7154
Full text not available from this repository. (Request a copy)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 a fixed contact angle alpha is an element of (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.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | ELASTIC CURVES; EXISTENCE; EVOLUTION; L-2-FLOW; SOBOLEV; SPACES; curve diffusion; surface diffusion; contact angles; weighted Sobolev spaces; blow-up criteria |
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics Mathematics > Prof. Dr. Helmut Abels |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 07 Apr 2021 06:29 |
| Last Modified: | 07 Apr 2021 06:29 |
| URI: | https://pred.uni-regensburg.de/id/eprint/45470 |
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