Abstract
We consider a quasi-static droplet motion based on contact angle dynamics on a planar surface. We derive a natural time-discretization and prove the existence of a weak global-in-time solution in the continuum limit. The time discrete interface motion is described in comparison with barrier functions, which are classical sub- and super-solutions in a local neighborhood. This barrier property is different from standard viscosity solutions since there is no comparison principle for our problem. In the continuum limit the barrier properties still hold in a modified sense.
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Acknowledgments
Natalie Grunewald was supported by the German Science Foundation, DFG, through fellowship GR 3391/1-1. Inwon Kim is supported by NSF DMS 0700732. The authors thank Karl Glasner for helpful discussions. Natalie Grunewald thanks UCLA for its hospitality during her stay in the last year, during which most of this paper was written.
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Communicated by L. Ambrosio.
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Open Access This is an open access article distributed under the terms of the Creative Commons Attribution Noncommercial License (https://creativecommons.org/licenses/by-nc/2.0), which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.
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Grunewald, N., Kim, I. A variational approach to a quasi-static droplet model. Calc. Var. 41, 1–19 (2011). https://doi.org/10.1007/s00526-010-0351-1
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DOI: https://doi.org/10.1007/s00526-010-0351-1