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

DOI10.1134/S1064562408030198zbMath1148.49019OpenAlexW2127710576MaRDI QIDQ954200

Vladimir Il'in

Publication date: 10 November 2008

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

Full work available at URL: https://doi.org/10.1134/s1064562408030198

zbMATH Keywords

wave equationstringanalytic form of an optimal boundary control

Mathematics Subject Classification ID

Optimality conditions for problems involving partial differential equations (49K20) Vibrations in dynamical problems in solid mechanics (74H45) Wave equation (35L05) Strings (74K05)

Related Items (3)

Mixed problems for the string vibration equation with nonlocal conditions of the general form at the right endpoint and with an inhomogeneous condition at the left endpoint ⋮ Optimal boundary control of string vibrations with a model nonlocal boundary condition of one of two types ⋮ Four mixed problems for the vibrating string equation with boundary and nonlocal Dirichlet and Neumann conditions

Cites Work

• Optimization of a boundary control by a displacement at one end of a string based on minimization of the integral of the modulus of the derivative of the displacement raised to an arbitrary power \(p \geq 1\)
• Optimization of a boundary control by a displacement at one end of a string with second end free during an arbitrary sufficiently large time interval

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