On the one-dimensional relativistic induction equation

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 (C) 2013 John Wiley & Sons, Ltd.