## 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

## Published In

## DOI

## EISSN

## ISSN

## Publication Date

## Volume

## Issue

## Start / End Page

## Related Subject Headings

- Mathematical Physics
- 5107 Particle and high energy physics
- 4904 Pure mathematics
- 4902 Mathematical physics
- 0206 Quantum Physics
- 0105 Mathematical Physics
- 0101 Pure Mathematics

### Citation

*Communications in Mathematical Physics*,

*81*(2), 203–227. https://doi.org/10.1007/BF01208895

*Communications in Mathematical Physics*81, no. 2 (June 1, 1981): 203–27. https://doi.org/10.1007/BF01208895.

*Communications in Mathematical Physics*, vol. 81, no. 2, June 1981, pp. 203–27.

*Scopus*, doi:10.1007/BF01208895.

## Published In

## DOI

## EISSN

## ISSN

## Publication Date

## Volume

## Issue

## Start / End Page

## Related Subject Headings

- Mathematical Physics
- 5107 Particle and high energy physics
- 4904 Pure mathematics
- 4902 Mathematical physics
- 0206 Quantum Physics
- 0105 Mathematical Physics
- 0101 Pure Mathematics