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

Brenier, Yann

Methods Appl. Anal. 11, No. 4, 515-532 (2004).

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.

Reviewer: Iuliana Oprea (Fort Collins)

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)

Keywords:

vibrating string; conservation laws; maximal monotone operators; Chaplygin-Born-Infeld (CBI) system; numerical scheme; maximal monotone operator theory