Solvability of the mixed problem for the wave equation with a dynamic boundary condition

DOI10.1134/S0012266112100096zbMath1259.35145OpenAlexW2126095658WikidataQ115252117 ScholiaQ115252117MaRDI QIDQ1935408

A. A. Kholomeeva, E. I. Moiseev

Publication date: 15 February 2013

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

Full work available at URL: https://doi.org/10.1134/s0012266112100096

Mathematics Subject Classification ID

PDEs in connection with mechanics of particles and systems of particles (35Q70) Boundary value problems for PDEs of mixed type (35M12)

Related Items (9)

Fourier method in a mixed problem for the wave equation on a graph ⋮ Factorized equation of vibrations of a finite string with nonstationary second directional derivatives at the endpoints ⋮ On an optimal boundary control problem with a dynamic boundary condition ⋮ Reconstruction of two functions in the model of vibrations of a string one end of which is placed in a moving medium ⋮ Unnamed Item ⋮ Optimal boundary displacement control at one end of a string with a medium exerting resistance at the other end ⋮ Boundary displacement control for the oscillation process with boundary conditions of damping type for a time less than critical ⋮ Estimation of the time-dependent body force needed to exert on a membrane to reach a desired state at the final time ⋮ Inhomogeneous factorized second-order hyperbolic equation in a quarter of the plane with a seminonstationary factorized second directional derivative in the boundary condition

Cites Work

• Solvability of mixed problems for the string oscillation equation in the space \(W_{p}^{1}\), with \(p \geq 1\)
• Optimal boundary force control at one end of a string for a given displacement mode at the other end
• Mixed problem for the string vibration equation with a time-dependent oblique derivative in the boundary condition

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