Jump discontinuities of semilinear, strictly hyperbolic systems in two variables: Creation and propagation

The creation and propagation of jump discontinuities in the solutions of semilinear strictly hyperbolic systems is studied in the case where the initial data has a discrete set, {xi}i^{=1 n}, 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}i^{=1 n}. (iii) if two forward characteristics in S intersect, then 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 forward characteristics from an intersection point. We prove a sufficient condition which guarantees that in many cases the lower bound is also an upper bound. © 1981 Springer-Verlag.

Duke Scholars

Author Michael C. Reed Mathematics