1. This paper is devoted to the study of wave fronts of solutions of first order symmetric systems of non-linear partial differential equations. A short communication was published in [4]. The microlocal point of view enables us to obtain more precise information concerning the smoothness of solutions of symmetric hyperbolic systems. Our main result is a generalization to the non-linear case of Theorem 1.1 of Ivriĭ [3]. The machinery of paradifferential operators introduced by Bony [1] together with an idea coming from [3], [2] are used.
@article{bwmeta1.element.bwnjournal-article-bcpv27z2p361bwm,
author = {Popivanov, P.},
title = {Wave fronts of solutions of some classes of non-linear partial differential equations},
journal = {Banach Center Publications},
volume = {27},
year = {1992},
pages = {361-366},
zbl = {0820.35029},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-bcpv27z2p361bwm}
}
Popivanov, P. Wave fronts of solutions of some classes of non-linear partial differential equations. Banach Center Publications, Tome 27 (1992) pp. 361-366. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-bcpv27z2p361bwm/
[000] [1] J. M. Bony, Calcul symbolique et propagation des singularités pour les équations aux dérivées partielles non-linéaires, Ann. Sci. Ecole Norm. Sup. (4) 14 (1981), 209-246. | Zbl 0495.35024
[001] [2] L. Hörmander, The Analysis of Linear Partial Differential Operators IV, Springer, Berlin 1985. | Zbl 0612.35001
[002] [3] V. I. Ivriĭ, Wave fronts of solutions of symmetric pseudodifferential systems, Sibirsk. Mat. Zh. 20 (1979), 557-578 (in Russian).
[003] [4] P. Popivanov, Wave fronts of the solutions of some classes of non-linear partial differential equations, C. R. Acad. Bulgare Sci. 40 (11) (1987), 27-28. | Zbl 0682.35066