Family of implicit schemes uniformly controllable for the 1-D wave equation.

DOI10.1016/j.crma.2004.09.037zbMath1061.65054OpenAlexW1981100151MaRDI QIDQ1763499

Arnaud Münch

Publication date: 22 February 2005

Published in: Comptes Rendus. Mathématique. Académie des Sciences, Paris (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.crma.2004.09.037

zbMATH Keywords

stabilitycontrollabilitywave equationfinite difference schemesFourier seriesCourant-Friedrichs-Levy conditionIngham's inequality

Mathematics Subject Classification ID

Numerical optimization and variational techniques (65K10) Controllability (93B05) Control/observation systems governed by partial differential equations (93C20) Lyapunov and other classical stabilities (Lagrange, Poisson, (L^p, l^p), etc.) in control theory (93D05) Wave equation (35L05)

Related Items

Uniformly controllable schemes for the wave equation on the unit square ⋮ A uniformly controllable and implicit scheme for the 1-D wave equation ⋮ An application of moment method to uniform boundary controllability property of a semidiscrete 1-d wave equation with a lower rate vanishing viscosity ⋮ An Ingham type proof for a two-grid observability theorem ⋮ Observability inequality for the finite-difference semi-discretization of the 1-d coupled wave equations ⋮ Optimal filtration for the approximation of boundary controls for the one-dimensional wave equation using a finite-difference method ⋮ Optimal approximation of internal controls for a wave-type problem with fractional Laplacian using finite-difference method

Cites Work

• Boundary controllability of a linear semi-discrete 1-D wave equation derived from a mixed finite element method
• Discrete Ingham inequalities and applications.
• Uniform boundary controllability of a semi-discrete 1-D wave equation
• Uniform boundary controllability of a discrete 1-D wave equation
• A numerical approach to the exact boundary controllability of the wave equation (I) Dirichlet controls: Description of the numerical methods
• Dispersion-corrected explicit integration of the wave equation
• Unnamed Item