Optimization of a control by an elastic boundary force during an arbitrary sufficiently large time interval \(T\) at one end of a string with second end free

DOI10.1134/S1064562407060142zbMath1151.49005OpenAlexW1969212991MaRDI QIDQ957811

E. I. Moiseev, Vladimir Il'in

Publication date: 1 December 2008

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

Full work available at URL: https://doi.org/10.1134/s1064562407060142

zbMATH Keywords

generalized solution of the wave equationboundary control by an elastic forcestring oscillations

Mathematics Subject Classification ID

Initial-boundary value problems for second-order hyperbolic equations (35L20) Wave equation (35L05) Existence theories for optimal control problems involving partial differential equations (49J20) Strings (74K05)

Related Items (3)

The independence of optimal boundary controls of string oscillations from the choice of a point of compatibility of the initial and final conditions ⋮ Uniqueness theorems for generalized solutions to four mixed problems for the wave equation with nonlocal boundary conditions ⋮ Optimization of an optimal boundary control by an elastic force at one end of a string under a model nonlocal boundary condition of one of four types

Cites Work

• Optimization of a boundary control of an elastic force at one end of a string based on minimization of the integral of the modulus of the elastic force raised to an arbitrary power \(p \geq 1\)
• 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 \(p \geq 1\)
• Minimization of the \(L_{p}\)-norm with arbitrary \(p \geq 1\) of the derivative of a boundary displacement control on an arbitrary sufficiently large time interval t

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