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Order preserving vibrating strings and applications to electrodynamics and magnetohydrodynamics. (English) Zbl 1107.74028

The author studies the motion of a system of vertical strings subjected to horizontal vibrations in the plane, with the help of a system of first order conservation laws, the so-called Chaplygin-Born-Infeld (CBI) system. A numerical scheme is introduced to maintain order preserving strings beyond singularities; it is shown, using maximal monotone operator theory, that the order preserving scheme is convergent to the vanishing viscosity limit of the CBI system.

MSC:

74K05 Strings
76W05 Magnetohydrodynamics and electrohydrodynamics
35L70 Second-order nonlinear hyperbolic equations
74H45 Vibrations in dynamical problems in solid mechanics
78A25 Electromagnetic theory (general)
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