| Contents |
| New analytic methods for a large class of quasilinear exterior elliptic--hyperbolic systems are discussed. These include a method for generating B\"{a}cklund transformations and a method for contructing explicit solutions on both sides of the parabolic transition. In addition, we prove the well-posedness of boundary value problems for steady flows having nonzero vorticity; such problems are characterized by a degeneration of ellipticity near the sonic speed. All these methods use properties of the Hodge duality operator in an essential way. |
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