Boundary control problem for the one-dimensional Klein-Gordon-Fock equation with a variable coefficient: the case of control by displacements at two endpoints

DOI10.1134/S0012266113080090zbMath1278.93047OpenAlexW1963891244WikidataQ115251977 ScholiaQ115251977MaRDI QIDQ389334

M. F. Abdukarimov, Leonid V. Kritskov

Publication date: 20 January 2014

Published in: Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1134/s0012266113080090

zbMATH Keywords

variable coefficientboundary control problemone-dimensional Klein-Gordon-Fock equationarbitrary initial statearbitrary terminal statetwo endpoints

Mathematics Subject Classification ID

Controllability (93B05) Control/observation systems governed by partial differential equations (93C20) Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05)

Related Items (8)

Approximate solution to a time optimal boundary control problem for the wave equation ⋮ Approximations to time-optimal boundary controls for weak generalized solutions of the wave equation ⋮ Problem of boundary control by an elastic force on one end with the other end fixed for the telegraph equation with a variable coefficient ⋮ Continuous invertibility of a boundary control operator for the wave equation on subcritical intervals in classes of weak generalized solutions ⋮ Stability of a solution to one combined mixed problem for the Klein-Gordon-Fock equation with a variable coefficient ⋮ On boundary control problems for the Klein-Gordon-Fock equation with an integrable coefficient ⋮ On the nonexistence conditions of solution of two-point in time problem for nonhomogeneous PDE ⋮ Boundary control of string vibrations in a subcritical time under a medium resistance at the right end

Cites Work

• Boundary control problem for the one-dimensional Klein-Gordon-Fock equation with a variable coefficient. The case of control by displacement at one endpoint with the other endpoint being fixed
• Exact controllability for the semilinear wave equation
• Boundary control of the vibrations of a string at two endpoints under the condition of the existence of finite energy.
• On the Fourier method for solving a control problem for string oscillation
• Exact Controllability, Stabilization and Perturbations for Distributed Systems
• Two-endpoint boundary control of vibrations described by a finite-energy generalized solution of the wave equation
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