Jump discontinuities of semilinear,strictly hyperbolic systems in two variables: Creation and propagation |
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Authors: | Jeffrey Rauch Michael Reed |
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Institution: | 1. Department of Mathematics, University of Michigan, 48109, Ann Arbor, MI, USA 2. Department of Mathematics, Duke University, 27706, Durham, NC, USA
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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, {x i } i =1n , of jump discontinuities. LetS be the smallest closed set which satisfies: - S is a union of forward characteristics.
- S contains all the forward characteristics from the points {x i } i =1n .
- if two forward characteristics inS intersect, then all forward characteristics from the point of intersection lie inS.
We prove that the singular support of the solution lies inS. 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. |
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