Overdamped dynamics of a falling inextensible network: Existence of solutions
Ayk Telciyan
University of Coimbra, PortugalDmitry Vorotnikov
University of Coimbra, Portugal
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Abstract
We study the equations of overdamped motion of an inextensible triod with three fixed ends and a free junction under the action of gravity. The problem can be expressed as a system of PDEs that involves unknown Lagrange multipliers and non-standard boundary conditions related to the freely moving junction. It can also be formally interpreted as a gradient flow of the potential energy on a certain submanifold of the Otto–Wasserstein space of probability measures. We prove global existence of generalized solutions to this problem.
Cite this article
Ayk Telciyan, Dmitry Vorotnikov, Overdamped dynamics of a falling inextensible network: Existence of solutions. Interfaces Free Bound. 25 (2023), no. 3, pp. 343–372
DOI 10.4171/IFB/492