A Boundary Value Problem for Cold Plasma Dynamics

A characteristic feature of wave propagation in cold plasma is the possibility that a hybrid resonance surface, along which the linearized equation for the scalar potential changes from elliptic to hyperbolic type, may be tangent to a flux surface. This property can be represented in two dimensions by setting the hybrid resonance curve tangent to the line x = 0 at the origin of coordinates. The situation is somewhat different from that found in, for example, linear models of transonic fluid dynamics, see (1.6). In that case the sonic line is everywhere normal to the line x = 0. A model for such a resonance curve is the equation