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Erschienen in:
2012 | OriginalPaper | Buchkapitel
Light Near a Caustic
verfasst von : Thomas H. Otway
Erschienen in: The Dirichlet Problem for Elliptic-Hyperbolic Equations of Keldysh Type
Verlag: Springer Berlin Heidelberg
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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.