Energy inequalities for a model of wave propagation in cold plasma

Details Energy inequalities for a model of wave propagation in cold plasma Energy inequalities for a model of wave propagation in cold plasma

2005-04-26

arxiv.org/abs/math-ph/0504077v5

Publ. Mat. 52(1), 195-234 (2008)

Physics

Mathematical Physics

33 pages

Scientific paper

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.

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