Optimal boundary control of string vibrations with a model nonlocal boundary condition of one of two types

DOI10.1134/S1064562411020098zbMath1234.35268OpenAlexW2001029905MaRDI QIDQ656275

A. A. Kholomeeva

Publication date: 17 January 2012

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

Full work available at URL: https://doi.org/10.1134/s1064562411020098

zbMATH Keywords

nonlocal boundary conditionoptimal boundary controlstring vibrationclassical solution of wave equationweak solution on wave equation

Mathematics Subject Classification ID

Vibrations in dynamical problems in solid mechanics (74H45) Wave equation (35L05) Strings (74K05) PDEs in connection with mechanics of deformable solids (35Q74) Classical solutions to PDEs (35A09)

Related Items (5)

Existence of solutions for nonlinear fractional \(q\)-difference integral equations with two fractional orders and nonlocal four-point boundary conditions ⋮ Optimal boundary force control at one end of a string for a given displacement mode at the other end ⋮ Optimal boundary control by a force at one end of a string with a given force mode at the other end ⋮ Optimization of the boundary control of string vibrations at one string end with a given mode at the other end ⋮ The inverse problem for the nonhomogeneous oscillation equation on a half-line with a boundary condition of the third kind

Cites Work

• Optimal boundary control by an elastic force at one end and a displacement at the other end for an arbitrary sufficiently large time interval in the string vibration problem
• An analytic form of an optimal boundary control by displacement at one end of a string under a model nonlocal boundary condition of one of four types
• Boundary displacement control at one end of a string in the presence of a nonlocal boundary condition of one of four types, and its optimization
• Optimal boundary displacement control of string vibrations with a nonlocal oddness condition of the first kind

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