Math @ Duke

Publications [#244032] of Michael C. Reed
Papers Published
 Rauch, J; Reed, M, Jump discontinuities of semilinear, strictly hyperbolic systems in two variables: Creation and propagation,
Communications in Mathematical Physics, vol. 81 no. 2
(1981),
pp. 203227, ISSN 00103616 [doi]
(last updated on 2018/05/27)
Abstract: 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 SpringerVerlag.


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