Kentaro Saji
Abstract
We give useful criteria for lips, beaks and swallowtail singularities of a smooth map from the plane into the plane. As an application of the criteria, we discuss the singularities for a Cauchy problem of single conservation law.
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We give useful criteria for lips, beaks and swallowtail singularities of a smooth map from the plane into the plane. As an application of the criteria, we discuss the singularities for a Cauchy problem of single conservation law.
Key concepts: Gravitational singularity, Plane (geometry), Mathematics, Cauchy distribution, Complex plane, Mathematical analysis, Geometry