Threshold optimization in observability inequality for the wave equation with homogeneous Robin-type boundary condition

DOI10.1134/S0081543812040153zbMath1295.93020OpenAlexW2155644138MaRDI QIDQ742260

A. A. Dryazhenkov, M. M. Potapov

Publication date: 18 September 2014

Published in: Proceedings of the Steklov Institute of Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1134/s0081543812040153

zbMATH Keywords

wave equation with variable coefficientsconstructive observability inequalitiescontrollability-observability thresholdone-side boundary controlsstable approximate solutions

Mathematics Subject Classification ID

Controllability (93B05) Control/observation systems governed by partial differential equations (93C20) Observability (93B07) Wave equation (35L05)

Related Items (9)

Approximate solution to a time optimal boundary control problem for the wave equation ⋮ Numerical method for a quadratic minimization problem with an ellipsoidal constraint and an a priori estimate for the solution norm ⋮ Constructive observability inequalities for weak generalized solutions of the wave equation with elastic restraint ⋮ Approximations to time-optimal boundary controls for weak generalized solutions of the wave equation ⋮ Continuous invertibility of a boundary control operator for the wave equation on subcritical intervals in classes of weak generalized solutions ⋮ Numerical method for damping string vibrations with unknown initial state in the class of weak generalized solutions ⋮ Numerical solution of the positional boundary control problem for the wave equation with unknown initial data ⋮ Observability inequality for a wave equation with elastic fastening in the case of critical time interval ⋮ Problems of two-sided boundary control for the wave equation on subcritical intervals in classes of strong generalized solutions

Cites Work

• Non homogeneous boundary value problems for second order hyperbolic operators
• A stable method for solving linear equations with nonuniformly perturbed operator
• Exact Controllability of the One-Dimensional Wave Equation with Locally Distributed Control
• Propagation, Observation, and Control of Waves Approximated by Finite Difference Methods
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