Unique solutions to boundary value problems in the cold plasma model
Thomas H. Otway
TL;DR
This paper proves the unique existence of solutions for boundary value problems in cold plasma models, demonstrating well-posedness for certain domains and boundary conditions related to electromagnetic wave propagation.
Contribution
It establishes the existence and uniqueness of solutions for mixed elliptic-hyperbolic equations in cold plasma models, extending the mathematical understanding of these physical phenomena.
Findings
Unique solutions for homogeneous Dirichlet problems on D-star-shaped domains
Strong solutions for open boundary value problems in cold plasma models
Mathematical framework applicable to electromagnetic wave propagation in plasma
Abstract
The unique existence of a weak solution to the homogeneous closed Dirichlet problem on certain D-star-shaped domains is proven for a mixed elliptic-hyperbolic equation. Equations of this kind arise in models for electromagnetic wave propagation in cold plasma. A related class of open boundary value problems is shown to possess strong solutions.
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Taxonomy
TopicsAdvanced Mathematical Physics Problems · Differential Equations and Boundary Problems · Spectral Theory in Mathematical Physics