Boundary Stabilization of Numerical Approximations of the 1-D Variable Coefficients Wave Equation: A Numerical Viscosity Approach

DOI10.1007/978-3-319-08025-3_9zbMath1322.65091OpenAlexW141365134MaRDI QIDQ5264978

Aurora Marica, Enrique Zuazua

Publication date: 21 July 2015

Published in: Lecture Notes in Computational Science and Engineering (Search for Journal in Brave)

Full work available at URL: http://hdl.handle.net/20.500.11824/233

zbMATH Keywords

artificial viscosityfinite difference approximationsmultiplier techniquenumerical experimentboundary stabilization1-D wave equation with variable coefficients

Mathematics Subject Classification ID

Wave equation (35L05) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12)

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Output feedback stabilization for 1-D wave equation with variable coefficients and non-collocated observation ⋮ Propagation of 1D waves in regular discrete heterogeneous media: a Wigner measure approach ⋮ The exponential stabilization of a heat-wave coupled system and its approximation

Cites Work

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• Uniform null-controllability for the one-dimensional heat equation with rapidly oscillating periodic density
• Uniform boundary stabilization of the finite difference space discretization of the 1-D wave equation
• Propagation of 1D waves in regular discrete heterogeneous media: a Wigner measure approach
• Perfectly matched layers in 1-D: Energy decay for continuous and semi-discrete waves
• Uniformly exponentially stable approximations for a class of damped systems
• A direct method for the boundary stabilization of the wave equation
• Exponential decay for the semilinear wave equation with localized damping in unbounded domains
• Concentration and lack of observability of waves in highly heterogeneous media
• Weak observability estimates for 1-D wave equations with rough coefficients
• On the null controllability of the one-dimensional heat equation with BV coefficients
• A generalized internal control for the wave equation in a rectangle
• Exponential Decay for The Semilinear Wave Equation with Locally Distributed Damping
• A numerical approach to the exact boundary controllability of the wave equation (I) Dirichlet controls: Description of the numerical methods
• A Carleman estimates based approach for the stabilization of some locally damped semilinear hyperbolic equations
• Observability properties of a semi-discrete 1d wave equation derived from a mixed finite element method on nonuniform meshes
• Uniform Exponential Decay for Viscous Damped Systems*
• Uniform Boundary Controllability of a Semidiscrete 1-D Wave Equation with Vanishing Viscosity
• Control of Wave Processes with Distributed Controls Supported on a Subregion
• Sharp Sufficient Conditions for the Observation, Control, and Stabilization of Waves from the Boundary
• Numerical meshes ensuring uniform observability of one-dimensional waves: construction and analysis
• The rate at which energy decays in a string damped at one end
• Propagation, Observation, and Control of Waves Approximated by Finite Difference Methods
• On the Asymptotic Spectrum of Finite Element Matrix Sequences
• Convex Analysis
• Differentiation Under the Integral Sign