Geodesic
Overdamped dynamics of a falling inextensible network: Existence of solutions
Ayk Telciyan1 ; Dmitry Vorotnikov1
1University of Coimbra, Portugal
Interfaces and free boundaries, Tome 25 (2023) no. 3, pp. 343-372

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DOI

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.
DOI : 10.4171/ifb/492
Classification : 35-XX, 58-XX
Mots-clés : gradient flow, triod, curvature, inextensible string, unknown Lagrange multiplier

Ayk Telciyan  1   ; Dmitry Vorotnikov  1

1 University of Coimbra, Portugal 
Ayk Telciyan; Dmitry Vorotnikov. Overdamped dynamics of a falling inextensible network: Existence of solutions. Interfaces and free boundaries, Tome 25 (2023) no. 3, pp. 343-372. doi: 10.4171/ifb/492
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     title = {Overdamped dynamics of a falling inextensible network: {Existence} of solutions},
     journal = {Interfaces and free boundaries},
     pages = {343--372},
     year = {2023},
     volume = {25},
     number = {3},
     doi = {10.4171/ifb/492},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/ifb/492/}
}
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