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.
"Criteria for singularities of smooth maps from the plane into the plane and their applications." Hiroshima Math. J. 40 (2) 229 - 239, July 2010. https://doi.org/10.32917/hmj/1280754423