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Light Near a Caustic

  • Thomas H. Otway
Chapter
Part of the Lecture Notes in Mathematics book series (LNM, volume 2043)

Abstract

In the cold plasma model the sonic curve is a parabola. In the physical model presented in this chapter the sonic curve is a circle, and the elliptic region of the governing equation surrounds the hyperbolic region. Thus we can prescribe Dirichlet data on a suitable closed curve lying entirely in the elliptic region and obtain an elliptic–3hyperbolic boundary value problem. Eventually,we will construct such a problem and show that it possesses a weak solution. In the next chapter the sonic curve will also be a circle; but in that case the hyperbolic region of the governing equation will enclose the elliptic region, leading to a significant reduction in regularity for elliptic–hyperbolic Dirichlet problems.

Keywords

Eikonal Equation Elliptic Region Hyperbolic Region Minimal Surface Equation Uniform Asymptotic Expansion 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Thomas H. Otway
    • 1
  1. 1.Department of Mathematical SciencesYeshiva UniversityNew YorkUSA

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