1,051 research outputs found
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
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
Energy inequalities for a model of wave propagation in cold plasma
Energy inequalities are derived for an elliptic-hyperbolic operator arising
in plasma physics. These inequalities imply the existence of distribution and
weak solutions to various closed boundary-value problems. An existence theorem
is proven for a related class of Keldysh equations, and the failure of expected
methods for obtaining uniqueness is discussed. The proofs use ideas recently
introduced by Lupo, Morawetz, and Payne for a generalized Tricomi operator. The
existence of strong solutions under open boundary conditions is also proven.Comment: 33 page
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