Abstract
A weak Guderley‐Morawetz problem is formulated for a mixed elliptic‐hyperbolic system that arises in models of wave propagation in cold plasma. Weak solutions are shown to exist in a weighted Hilbert space. This result extends the work of Yamamoto (1994).
Highlights
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
As it is not clear that projective invariance has any physical meaning in the context of cold plasma dynamics, this analogy will not be pursued
Summary
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. Copyright c 2003 Hindawi Publishing Corporation Journal of Applied Mathematics 2003:1 (2003) 17–33 2000 Mathematics Subject Classification: 35M10, 35D05
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