Asymmetric exact controllability for networks of spatial elastic strings, springs and masses
Leugering G, Rodriguez C, Wang Y (2026)
Publication Type: Journal article
Publication year: 2026
Journal
Book Volume: 215
Article Number: 103963
DOI: 10.1016/j.matpur.2026.103963
Abstract
We consider networks of elastic strings with end masses, where the coupling is modeled via elastic springs. The model is representative of a network of nonlinear strings in which the strings are coupled to elastic bodies. The coupled system converges to the classical string-network model with Kirchhoff and continuity transmission conditions as the spring stiffness terms tend to infinity and the masses at the nodes vanish. Due to the presence of point masses at the nodes, the boundary conditions become dynamic and the corresponding first-order system of quasilinear balance laws exhibits nonlocal boundary conditions. We demonstrate well-posedness in the sense of semi-global classical solutions, namely on arbitrarily large time intervals provided that the initial and boundary data are sufficiently small, and we observe additional regularity at the masses. We prove local and global-local exact boundary controllability of a star-like network when controls are active at the endpoints of the string-spring-mass system except for one clamped end. At multiple nodes, a complex smoothing pattern appears, leading to asymmetric control spaces when springs and masses are present. Furthermore, the rank of the Laplacian matrix at the junction is crucial for controllability, particularly in models containing wave equations with degeneration at dynamic boundaries, which may be interpreted as damage in mechanical vibration systems where some springs are missing.
Authors with CRIS profile
Günter Leugering
Lehrstuhl für Angewandte Mathematik
Charlotte Rodriguez
Lehrstuhl für Angewandte Mathematik
Yue Wang
Involved external institutions
China (CN)How to cite
APA:
Leugering, G., Rodriguez, C., & Wang, Y. (2026). Asymmetric exact controllability for networks of spatial elastic strings, springs and masses. Journal De Mathematiques Pures Et Appliquees, 215. https://doi.org/10.1016/j.matpur.2026.103963
MLA:
Leugering, Günter, Charlotte Rodriguez, and Yue Wang. "Asymmetric exact controllability for networks of spatial elastic strings, springs and masses." Journal De Mathematiques Pures Et Appliquees 215 (2026).
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