Duality methods for a class of quasilinear systems

Duality methods are used to generate explicit solutions to nonlinear Hodge systems, demonstrate the well-posedness of boundary value problems, and reveal, via the Hodge-B\"acklund transformation, underlying symmetries among superficially different forms of the equations.Comment: 14 page

Maps and fields with compressible density

Properties of steady compressible flow for which geometric constraints have been placed on the potential function are derived, under hypotheses on the flow density and the singular set. Some related unconstrained problems are also considered, including the estimation of a class of fields having nonzero vorticity.Comment: 23 pages, tcilate

A boundary-value problem for cold plasma dynamics

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 work by Yamamoto.Comment: 18 pages, tcilate