The Riesz basis property of the system of root vectors for the equation of a nonhomogeneous damped string: Transformation operator method

DOI10.4310/MAA.1999.v6.n4.a9zbMath0986.74039MaRDI QIDQ1582352

Marianna A. Shubov

Publication date: 11 June 2002

Published in: Methods and Applications of Analysis (Search for Journal in Brave)

zbMATH Keywords

Riesz basisHilbert spaceeigenvectorsenergy spacesnonselfadjoint operatorsroot vectorsnonhomogeneous stringspectral decomposition theoremdistributed viscous dampingfirst-order dampinglinear nonselfadjoint boundary conditionsone-dimensional hyperbolic equations

Mathematics Subject Classification ID

Vibrations in dynamical problems in solid mechanics (74H45) Completeness of eigenfunctions and eigenfunction expansions in context of PDEs (35P10) Strings (74K05)

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Joint state and parameter estimation for distributed mechanical systems ⋮ Existence and Boundary Control of a Nonlinear Axially Moving String Subject to Disturbances ⋮ A Fourier series solution for the longitudinal vibrations of a bar with viscous boundary conditions at each end ⋮ Existence and stabilization of a Kirchhoff moving string with a distributed delay in the boundary feedback ⋮ Existence and stabilization of a Kirchhoff moving string with a delay in the boundary or in the internal feedback ⋮ The expansion of a semigroup and a Riesz basis criterion ⋮ Asymptotics of eigenfrequencies and eigenmodes of non-homogeneous inextensible filament with an end load ⋮ The damped string problem revisited ⋮ Stabilization of wave systems with input delay in the boundary control

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