Abstract
AbstractWe consider a parabolic obstacle problem for Euler’s elastic energy of graphs with fixed ends. We show global existence, well-posedness and subconvergence provided that the obstacle and the initial datum are suitably ‘small’. For symmetric cone obstacles we can improve the subconvergence to convergence. Qualitative aspects such as energy dissipation, coincidence with the obstacle and time regularity are also examined.
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,Control and Optimization
Reference25 articles.
1. Andrews, G.E., Askey, R., Roy, R.: Special functions, Encyclopedia of Mathematics and its Applications, 71, Cambridge University Press, Cambridge, pp. xvi+664. (1999). https://doi.org/10.1017/CBO9781107325937
2. Ambrosio, L., Gigli, N.: A user’s guide to optimal transport, Modelling and optimisation of flows on networks. Lecture Notes in Math. 2062, Springer, Heidelberg, pp. 1–155. (2013). https://doi.org/10.1007/978-3-642-32160-3
3. Ambrosio, L., Gigli, N., Savaré, G.: Gradient flows in metric spaces and in the space of probability measures. Lectures in Mathematics ETH Zürich, 2, Birkhäuser Verlag, Basel, pp. x+334 (2008)
4. article Athanasopoulos, I., Caffarelli, L., Milakis, E.: Parabolic obstacle problems, quasi-convexity and regularity. Ann. Soc. Norm. Super. Pisa Cl. Sci. (5), 19, 2, 781–825 (2019)
5. Blatt, S., Hopper, C., Vorderobermeier, N.: A minimising movement scheme for the p-elastic energy of curves, Preprint. arXiv:2101.10101 (2021)
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