Stabilization of star-shaped networks of strings. (English) Zbl 1150.93537

Summary: We study the energy decay of a network of vibrating elastic strings where the strings are coupled at a common end in a star-shaped configuration. We prove that the solutions are not exponentially stable in the energy space. Moreover, we give explicit polynomial decay estimates valid for regular initial data. These estimates depend on the diophantine approximations properties of the lengths of the strings of the network.


93D15 Stabilization of systems by feedback
35B37 PDE in connection with control problems (MSC2000)
74M05 Control, switches and devices (“smart materials”) in solid mechanics
35L20 Initial-boundary value problems for second-order hyperbolic equations
74K05 Strings
93B07 Observability
93C20 Control/observation systems governed by partial differential equations