Light Near a Caustic

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


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.


Eikonal Equation Elliptic Region Hyperbolic Region Minimal Surface Equation Uniform Asymptotic Expansion 
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© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

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

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