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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.

MSC:

35M10 PDEs of mixed type
35D05 Existence of generalized solutions of PDE (MSC2000)
82D10 Statistical mechanics of plasmas
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