A boundary-value problem for cold plasma dynamics

TL;DR

This paper formulates and proves the existence of weak solutions for a boundary-value problem modeling wave propagation in cold plasma, extending previous work by Yamamoto in the context of mixed elliptic-hyperbolic systems.

Contribution

It introduces a weak Guderley-Morawetz problem for cold plasma dynamics and demonstrates the existence of solutions in a weighted Hilbert space, advancing mathematical understanding of plasma wave models.

Findings

Existence of weak solutions in a weighted Hilbert space.

Extension of Yamamoto's work to a new boundary-value problem.

Framework for analyzing wave propagation in cold plasma.

Abstract

A weak Guderley-Morawetz problem is formulated for a mixed elliptic-hyperbolic system that arises in models of wave propagation in cold plasma. Weak solutions are shown to exist in a weighted Hilbert space. This result extends work by Yamamoto.