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

DOI10.1134/S1064562408030241zbMath1148.49020OpenAlexW1979875684MaRDI QIDQ954205

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/s1064562408030241

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

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

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