M.: Jump discontinuities of semilinear, strictly hyperbolic equations in two variables: Creation and propagation

Abstract. The creation and propagation of jump discontinuities in the solu-tions of semilinear strictly hyperbolic systems is studied in the case where the initial data has a discrete set, {xi}~ = 1, of jump discontinuities. Let S be the smallest closed set which satisfies: (i) S is a union of forward characteristics. (ii) S contains all the forward characteristics from the points {xi}~ = 1" (iii) if two forward characteristics in S intersect, hen all forward characteristics from the point of intersection lie in S. We prove that the singular support of the solution lies in S. We derive a sum law which gives a lower bound on the smoothness of the solution across for-ward characteristics from an intersection point. We prove a sufficient condition which guarantees that in many cases the lower bound is also an upper bound. I