The Spectrum of the Damped Wave Operator for a Bounded Domain inR2

DOI10.1080/10586458.2003.10504494zbMath1061.35064OpenAlexW2013304260MaRDI QIDQ4811525

Gilles Lebeau, Mark Asch

Publication date: 6 September 2004

Published in: Experimental Mathematics (Search for Journal in Brave)

Full work available at URL: https://projecteuclid.org/euclid.em/1067634733

zbMATH Keywords

spectrumdamped wave equationnon-selfadjoint operatornumber of eigenvalues in a horizontal strip

Mathematics Subject Classification ID

Related Items (17)

Eigenvalue asymptotics for the damped wave equation on metric graphs ⋮ Exploring the spectra of some classes of singular integral operators with symbolic computation ⋮ Best decay rate, observability and open-loop admissibility costs: discussions and numerical study ⋮ Energy decay for the damped wave equation under a pressure condition ⋮ Sharp resolvent estimate for the damped-wave Baouendi-Grushin operator and applications ⋮ Semiclassical asymptotics for nonselfadjoint harmonic oscillators ⋮ Numerical Approximation of the Best Decay Rate for Some Dissipative Systems ⋮ Eigenmodes of the damped wave equation and small hyperbolic subsets ⋮ Nonselfadjoint Perturbations of Selfadjoint Operators in Two Dimensions II. Vanishing Averages ⋮ The damped string problem revisited ⋮ Uniform stabilization of a viscous numerical approximation for a locally damped wave equation ⋮ Optimal Absorption of Acoustic Waves by a Boundary ⋮ Weighted \(L^2\)-estimates for dissipative wave equations with variable coefficients ⋮ Eigenvalue asymptotics, inverse problems and a trace formula for the linear damped wave equation ⋮ Construction of quasimodes for non-selfadjoint operators via propagation of Hagedorn wave-packets ⋮ The geometrical quantity in damped wave equations on a square ⋮ Spectrum of a non-selfadjoint quantum star graph

Cites Work

• Ergodic properties of eigenfunctions for the Dirichlet problem
• Exponential Decay of Energy of Evolution Equations with Locally Distributed Damping
• Eigenvalues of the Laplacian in Two Dimensions
• Optimizing the Rate of Decay of Solutions of the Wave Equation Using Genetic Algorithms: A Counterexample to the Constant Damping Conjecture
• The rate at which energy decays in a damped String
• Exact Controllability of the Damped Wave Equation
• Asymptotic distribution of eigenfrequencies for damped wave equations

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