Energy inequalities for a model of wave propagation in cold plasma. (English) Zbl 1162.35428

Summary: 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.


35M10 PDEs of mixed type
35D05 Existence of generalized solutions of PDE (MSC2000)
82D10 Statistical mechanics of plasmas
Full Text: DOI arXiv EuDML