Premium
On the one‐dimensional relativistic induction equation
Author(s) -
Núñez Manuel
Publication year - 2013
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/mma.2987
Subject(s) - mathematics , mathematical analysis , magnetic diffusivity , induction equation , magnetohydrodynamics , dissipation , magnetic field , perturbation (astronomy) , physics , quantum mechanics
The induction equation of relativistic magnetohydrodynamics is considered as a singular perturbation problem for small magnetic diffusivity. When the quantities depend on a single space variable, the resulting hyperbolic equation may be studied with techniques of asymptotic analysis. Different approximations are found for initial, intermediate, and large times. The last case is the most difficult; the approximate magnetic flux function satisfies a certain parabolic equation. This equation is studied from the viewpoint of energy dissipation, providing clues on the behavior of the electric and magnetic fields. Copyright © 2013 John Wiley & Sons, Ltd.