Formation of singularities for Hamilton-Jacobi equation with several space variables (Q1174755)

This paper concerns the singularity unfolding of generalized solutions of the Hamilton-Jacobi equations in an arbitrary number of space dimensions. As with conservation laws, solutions to the Cauchy problem considered generally become multivalued after some finite time. The author examines the evolution of characteristics and uses singularity theory of smooth mappings in higher dimensional spaces to examine the structure of solutions, whose graphs are shown to admit swallow tails. He then goes on to employ a semi-concavity criterion to pick out a unique solution from the resulting triple possibility.