Polynomial stability for a system of coupled strings | Zendy

Rzepnicki Łukasz | Zendy; Schnaubelt Roland | Zendy

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Polynomial stability for a system of coupled strings

Author(s) -

Rzepnicki Łukasz,

Schnaubelt Roland

Publication year - 2018

Publication title -

bulletin of the london mathematical society

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 2.396

H-Index - 48

eISSN - 1469-2120

pISSN - 0024-6093

DOI - 10.1112/blms.12212

Subject(s) - mathematics , resolvent , exponent , polynomial , quotient , stability (learning theory) , boundary (topology) , mathematical analysis , pure mathematics , philosophy , linguistics , machine learning , computer science

We study the long‐time behavior of two vibrating strings which are coupled at a common boundary point by a damper. We show that the classical solutions converge polynomially with a uniform rate, where the decay exponent depends on number theoretic properties of the quotient of the wave speeds of the two springs. The proof is based on a resolvent characterization of polynomial stability due to Borichev–Tomilov and Batty–Duyckaerts.

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