Energy inequalities for a model of wave propagation in cold plasma

TL;DR

This paper establishes energy inequalities for a plasma wave model, proving existence of solutions and discussing uniqueness issues, thereby advancing mathematical understanding of wave propagation in cold plasma.

Contribution

It introduces new energy inequalities for an elliptic-hyperbolic operator in plasma physics and proves existence theorems for solutions to related boundary-value problems.

Findings

Energy inequalities are derived for the plasma wave operator.

Existence of distribution and weak solutions is established.

Failure of certain methods for uniqueness is discussed.

Abstract

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.