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Energy inequalities for a model of wave propagation in cold plasma

Thomas H. Otway

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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.

Article information

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

First available in Project Euclid: 17 December 2007

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 35M10: Equations of mixed type 35D05 82D10: Plasmas

Elliptic-hyperbolic equations energy inequalities closed boundary-value problems symmetric-positive operators equations of Keldysh type


Otway, Thomas H. Energy inequalities for a model of wave propagation in cold plasma. Publ. Mat. 52 (2008), no. 1, 195--234.

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