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Stabilization of generic trees of strings. (English) Zbl 1064.93034
Summary: The authors study the energy decay of a tree-shaped network of vibrating elastic strings when the pointwise feedback acts in the root of the tree. They show that the strings are not exponentially stable in the energy space. Moreover, explicit polynomial decay estimates valid for regular initial data are given.

MSC:
93D15 Stabilization of systems by feedback
35B37 PDE in connection with control problems (MSC2000)
93B07 Observability
74K05 Strings
35B40 Asymptotic behavior of solutions to PDEs
74M05 Control, switches and devices (“smart materials”) in solid mechanics
93C20 Control/observation systems governed by partial differential equations
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