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

• Autorzy: P. R. Popivanov
• Języki publikacji: EN

Abstrakty

EN

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.

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Banach Center Publications
• Rocznik: 1992
• Tom: 27
• Numer: 2
• Strony: 361-366

Daty

wydano

1992

Twórcy

autor

P. R. Popivanov

• Department of Mathematics, Sofia University, Bul. A. Ivanov 5, Sofia, Bulgaria

Bibliografia

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