Exponential and super stability of a wave network

DOI10.1007/s10440-012-9768-1zbMath1263.35043OpenAlexW1999101217MaRDI QIDQ1947020

Gen-Qi Xu, Ya Xuan Zhang

Publication date: 11 April 2013

Published in: Acta Applicandae Mathematicae (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10440-012-9768-1

zbMATH Keywords

spectrumcompletenessspectral decompositionexponentially stablesuper-stableno Riesz basis generationwave network

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Initial-boundary value problems for second-order hyperbolic equations (35L20) Stability in context of PDEs (35B35) Estimates of eigenvalues in context of PDEs (35P15) Completeness of eigenfunctions and eigenfunction expansions in context of PDEs (35P10) Initial-boundary value problems for second-order hyperbolic systems (35L53)

Related Items (10)

Networks of geometrically exact beams: well-posedness and stabilization ⋮ Existence, uniqueness and stabilization of solutions of a generalized telegraph equation on star shaped networks ⋮ On the finite-time Bhat-Bernstein feedbacks for the strings connected by point mass ⋮ Exponential stability of perturbed superstable systems in Hilbert spaces ⋮ The exponential decay rate of generic tree of 1-d wave equations with boundary feedback controls ⋮ A new approach for the stability analysis of wave networks ⋮ Spectral analysis for a degenerate tree and applications ⋮ Stability and spectral properties of general tree-shaped wave networks with variable coefficients ⋮ Finite-time stabilization of a network of strings ⋮ Exponential-stability and super-stability of a thermoelastic system of type II with boundary damping

Cites Work

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• A Sufficient Condition on Riesz Basis with Parentheses of Non--Self-Adjoint Operator and Application to a Serially Connected String System under Joint Feedbacks
• Abstract Second Order Hyperbolic System and Applications to Controlled Network of Strings

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