The Cauchy Problem for Semilinear Hyperbolic Equations with Cross Discontinuous Data

This paper is devoted to study Cauchy problems of multidimensional semilinear strictly hyperbolic equations of second order with strongly singular initial data, where the derivatives of the initial data have discontinuity on two smooth curves transversally intersecting each other. The existence of the solution is proved, meanwhile, it is precisely discribed the flowery structure of the singularity of the solution.