Wave fronts of solutions of some classes of non-linear partial differential equations

P. Popivanov

Banach Center Publications (1992)

  • Volume: 27, Issue: 2, page 361-366
  • ISSN: 0137-6934

Abstract

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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.

How to cite

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Popivanov, P.. "Wave fronts of solutions of some classes of non-linear partial differential equations." Banach Center Publications 27.2 (1992): 361-366. <http://eudml.org/doc/262575>.

@article{Popivanov1992,
abstract = {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.},
author = {Popivanov, P.},
journal = {Banach Center Publications},
keywords = {wave fronts of solutions},
language = {eng},
number = {2},
pages = {361-366},
title = {Wave fronts of solutions of some classes of non-linear partial differential equations},
url = {http://eudml.org/doc/262575},
volume = {27},
year = {1992},
}

TY - JOUR
AU - Popivanov, P.
TI - Wave fronts of solutions of some classes of non-linear partial differential equations
JO - Banach Center Publications
PY - 1992
VL - 27
IS - 2
SP - 361
EP - 366
AB - 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.
LA - eng
KW - wave fronts of solutions
UR - http://eudml.org/doc/262575
ER -

References

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  1. [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. Zbl0495.35024
  2. [2] L. Hörmander, The Analysis of Linear Partial Differential Operators IV, Springer, Berlin 1985. Zbl0612.35001
  3. [3] V. I. Ivriĭ, Wave fronts of solutions of symmetric pseudodifferential systems, Sibirsk. Mat. Zh. 20 (1979), 557-578 (in Russian). 
  4. [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. Zbl0682.35066

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