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Small vibrations of an elastic conductor in a magnetic field
Author(s) -
Wolfe Peter
Publication year - 1998
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/(sici)1099-1476(19981125)21:17<1559::aid-mma9>3.0.co;2-x
Subject(s) - uniqueness , mathematics , hyperbolic partial differential equation , mathematical analysis , conductor , partial differential equation , boundary value problem , motion (physics) , magnetic field , uniqueness theorem for poisson's equation , vibration , equations of motion , helmholtz equation , classical mechanics , physics , geometry , acoustics , quantum mechanics
In this paper we study the motion of an elastic conducting wire in a magnetic field. The motion of the conductor induces a current in the wire (Faraday's law) which, in turn produces a force on the wire. We consider the linear equation obtained by linearizing the resulting equations of motion about an equilibrium solution. This is a hyperbolic partial differential equation with a non‐local term. We prove existence and uniqueness of a weak solution of an initial–boundary value problem for this equation. © 1998 B. G. Teubner Stuttgart—John Wiley & Sons, Ltd.