TY - JOUR
T1 - The gradient flow of the potential energy on the space of arcs
AU - Shi, Wenhui
AU - Vorotnikov, Dmitry
PY - 2019/4/1
Y1 - 2019/4/1
N2 - We study the gradient flow of the potential energy on the infinite-dimensional Riemannian manifold of spatial curves parametrized by the arc length, which models overdamped motion of a falling inextensible string. We prove existence of generalized solutions to the corresponding nonlinear evolutionary PDE and their exponential decay to the equilibrium. We also observe that the system admits solutions backwards in time, which leads to non-uniqueness of trajectories.
AB - We study the gradient flow of the potential energy on the infinite-dimensional Riemannian manifold of spatial curves parametrized by the arc length, which models overdamped motion of a falling inextensible string. We prove existence of generalized solutions to the corresponding nonlinear evolutionary PDE and their exponential decay to the equilibrium. We also observe that the system admits solutions backwards in time, which leads to non-uniqueness of trajectories.
UR - http://www.scopus.com/inward/record.url?scp=85063163290&partnerID=8YFLogxK
U2 - 10.1007/s00526-019-1524-1
DO - 10.1007/s00526-019-1524-1
M3 - Article
AN - SCOPUS:85063163290
SN - 0944-2669
VL - 58
JO - Calculus of Variations and Partial Differential Equations
JF - Calculus of Variations and Partial Differential Equations
IS - 2
M1 - 59
ER -