Problems with a small parameter and propagation of fronts in the galactic dynamo theory

Propagation of the magnetic field to the periphery of the galactic disc and the possibility of its transfer using a dynamo wave are studied. For this purpose, a system of two equations with a small parameter of high-order derivatives is considered. Its important feature is that for a certain value of the independent variable the stability of the roots of the degenerate equation changes. For this problem the numerical velocity values of transition layers are obtained. The problem of their possible penetration beyond the bounds of the point of stability change is studied. A similar scalar equation is studied, for which asymptotic estimates of the front propagation velocity can be obtained. These estimates are in good agreement with the numerical simulation results.