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

DOI10.1134/S0012266117040097zbMath1372.35299WikidataQ115250971 ScholiaQ115250971MaRDI QIDQ2399392

Ilya S. Mokrousov

Publication date: 23 August 2017

Published in: Differential Equations (Search for Journal in Brave)

zbMATH Keywords

analytic representation of solutionsBitsadze-Samarskii boundary conditionfour mixed problems

Mathematics Subject Classification ID

Initial-boundary value problems for second-order hyperbolic equations (35L20) Vibrations in dynamical problems in solid mechanics (74H45) Solutions to PDEs in closed form (35C05) Strings (74K05) PDEs in connection with mechanics of deformable solids (35Q74)

Cites Work

• On four mixed problems for the string vibration equation with homogeneous nonlocal conditions
• 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
• 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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