• DOI:10.1137/060655134
• Corpus ID: 30194962

Weak Lacunae of Electromagnetic Waves in Dilute Plasma

@article{Tsynkov2007WeakLO,
  title={Weak Lacunae of Electromagnetic Waves in Dilute Plasma},
  author={Semyon Tsynkov},
  journal={SIAM J. Appl. Math.},
  year={2007},
  volume={67},
  pages={1548-1581}
}

• S. Tsynkov
• Published 12 September 2007
• Physics
• SIAM J. Appl. Math.

The propagation of waves is said to be diffusionless, and the corresponding governing PDE (or system) is said to satisfy Huygens' principle if the waves due to compactly supported sources have sharp aft fronts. The areas of no disturbance behind the aft fronts are called lacunae. Diffusionless propagation of waves is rare, whereas its opposite—diffusive propagation accompanied by aftereffects—is common. Nonetheless, lacunae can still be observed in a number of important applications, including the Maxwell equations in vacuum or in dielectrics with static response. In the framework of these applications, lacunae can be efficiently exploited for the numerical simulation of unsteady waves, and considerable progress has been made toward the development of lacunae-based methods for computational electromagnetism. Maxwell equations in vacuum are Huygens' because they reduce to a set of d'Alembert equations. Besides d'Alembert equations, there are no other scalar Huygens' equations in the standard $3+1$-dimensio...