EXISTENCE AND BIFURCATION OF VISCOUS PROFILES FOR ALL INTERMEDIATE MAGNETOHYDRODYNAMIC SHOCK-WAVES

A viscous profile for a magnetohydrodynamic shock wave is given by a h eteroclinic orbit of a six-dimensional gradient-like system of ordinar y differential equations. This system, and thus possibly the existence of a viscous profile, vary with an array delta of four positive dissi pation coefficients. It is known that for each choice of delta, all '' classical'' and ''degenerate intermediate'' shocks as well as some ''n ondegenerate intermediate'' shocks have viscous profiles, and that, vi ce versa, each given nondegenerate intermediate shock has no viscous p rofile for some range of delta. Complementing this picture, it is show n that (i) each nondegenerate intermediate shock does have a (family o f) viscous profile(s) for a certain other range of delta, and (ii) suc h profiles, for all intermediate shocks sharing the same relative flux , are generated in a global heteroclinic bifurcation. Both (i) and (ii ) are proved in a regime of delta in which the dissipative effects due to electrical resistivity and longitudinal viscosity dominate those a ssociated with transverse viscosity and heat conduction: The construct ive proof is based on a recently formulated method in geometric singul ar perturbation theory.