Differential and Integral Equations

Stabilization of star-shaped networks of strings

Kais Ammari and Mohamed Jellouli

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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.

Article information

Differential Integral Equations, Volume 17, Number 11-12 (2004), 1395-1410.

First available in Project Euclid: 21 December 2012

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 93D15: Stabilization of systems by feedback
Secondary: 35B37 35L20: Initial-boundary value problems for second-order hyperbolic equations 74K05: Strings 74M05: Control, switches and devices ("smart materials") [See also 93Cxx] 93B07: Observability 93C20: Systems governed by partial differential equations


Ammari, Kais; Jellouli, Mohamed. Stabilization of star-shaped networks of strings. Differential Integral Equations 17 (2004), no. 11-12, 1395--1410. https://projecteuclid.org/euclid.die/1356060252

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