Four mixed problems for the vibrating string equation with boundary and nonlocal Dirichlet and Neumann conditions

DOI10.1134/S106456240903017XzbMath1184.35100MaRDI QIDQ736017

A. A. Kuleshov

Publication date: 26 October 2009

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

zbMATH Keywords

weak solutionszero initial conditions

Mathematics Subject Classification ID

Initial-boundary value problems for second-order hyperbolic equations (35L20) Solutions to PDEs in closed form (35C05) Strings (74K05)

Cites Work

• 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
• 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
• Uniqueness of generalized solutions of mixed problems for the wave equation with nonlocal boundary conditions
• Optimization of a nonlocal boundary control of vibrations of a string with a fixed end for an arbitrary time interval that is a multiple of \(2l\)
• 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
• Two-endpoint boundary control of vibrations described by a finite-energy generalized solution of the wave equation

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