×
Delort, J. M.

Deuxième microlocalisation simultanée et front d’onde de produits. (The second simultaneous microlocalization and the wave front of products). (French) Zbl 0715.35049

Ann. Sci. Éc. Norm. Supér. (4) 23, No. 2, 257-310 (1990).
The author gives some description of the wave front set of a product of two distributions. He applies his result to examine certain nonlinear (pseudo) differential equations, for example a semilinear wave equation.
Reviewer: N.Jacob

Cited in 1 Review
Cited in 1 Document

MSC:

35L70 Second-order nonlinear hyperbolic equations
35S05 Pseudodifferential operators as generalizations of partial differential operators
46F10 Operations with distributions and generalized functions

Keywords:

second microlocalization; wave front set; semilinear wave equation
Cite Review PDF
Full Text: DOI Numdam EuDML

References:

[1] M. BEALS , Vector fields Associated to the Nonlinear Interaction of Progressing Waves (Indiana Univ. Math. J., vol. 37, n^\circ 3, 1988 , p. 637-666). MR 89m:35138 | Zbl 0644.35069 · Zbl 0644.35069 · doi:10.1512/iumj.1988.37.37031
[2] E. BIERSTONE et P. D. MILMAN , Semi-analytic and subanalytic Sets (Inst. Htes Etudes Sci. Publ. Math., n^\circ 67, 1988 , p. 5-42). Numdam | MR 89k:32011 | Zbl 0674.32002 · Zbl 0674.32002 · doi:10.1007/BF02699126
[3] J. M. BONY , Interaction des singularités pour les équations aux dérivées partielles non linéaires (Sém. Goulaouic-Meyer-Schwartz, exp. n^\circ 2, 1981 - 1982 ). Interaction des singularités pour les équations de Klein-Gordon non linéaires (Sém. Goulaouic-Meyer-Schwartz, exp. n^\circ 10, 1983 - 1984 ). Numdam | Zbl 0498.35017 · Zbl 0498.35017
[4] J. M. BONY , Second Microlocalization and Propagation of Singularities for Semi-linear Hyperbolic Equations (Taniguchi symp. HERT, Kotaka and Tokyo, 1984 , 11-49). MR 89e:35099 | Zbl 0669.35073 · Zbl 0669.35073
[5] J. M. DELORT et G. LEBEAU , Microfonctions I-lagrangiennes (J. Math. Pures et Appl., 67, 1988 , p. 39-84). MR 90a:58164 | Zbl 0659.46042 · Zbl 0659.46042
[6] L. HÖRMANDER , The Analysis of Linear Partial Differential Operators (Grundlehren der Mathematischen Wissenschaften, Springer-Verlag, 1983 ). Zbl 0521.35001 · Zbl 0521.35001
[7] M. KASHIWARA et P. SCHAPIRA , Micro-hyperbolic Systems (Acta Math., 142, 1979 , p. 1-55). MR 80b:58060 | Zbl 0413.35049 · Zbl 0413.35049 · doi:10.1007/BF02395056
[8] M. KASHIWARA et P. SCHAPIRA , Microlocal Study of Sheaves (Astérisque, 128, 1985 ). MR 87f:58159 | Zbl 0589.32019 · Zbl 0589.32019
[9] B. LASCAR et J. SJÖSTRAND , Equation de Schrödinger et propagation des singularités (Astérisque, 95, 1982 ). · Zbl 0529.58033
[10] Y. LAURENT , Problème de Cauchy 2-microdifférentiel et cycles évanescents , Prépublication de l’université Paris-Sud, 1988 .
[11] G. LEBEAU , Deuxième microlocalisation à croissance (Sém. Goulaouic-Meyer-Schwartz, exp. n^\circ 15, 1982 - 1983 ). Numdam | Zbl 0518.58037 · Zbl 0518.58037
[12] G. LEBEAU , Deuxième microlocalisation sur les sous-variétés isotropes (Ann. Inst. Fourier, Grenoble, vol. 35, (2), 1985 , p. 145-216). Numdam | MR 87h:58205 | Zbl 0539.58038 · Zbl 0539.58038 · doi:10.5802/aif.1014
[13] G. LEBEAU , Equations des ondes semi-linéaires II. Contrôle des singularités et caustiques non linéaires (Invent. math. 95, 1989 , p. 277-323). MR 92j:35126b | Zbl 0686.35015 · Zbl 0686.35015 · doi:10.1007/BF01393899
[14] G. LEBEAU , Front d’onde des fonctions non linéaires et polynômes (Séminaire E.D.P., exp. n^\circ 10, Ecole Polytechnique, 1988 - 1989 ). Numdam | Zbl 0698.35101 · Zbl 0698.35101
[15] A. MELIN et J. SJÖSTRAND , Fourier Integral Operators with Complex Valued Phase Functions (Springer Lect. Notes Math., 459, p. 121-223). Zbl 0306.42007 · Zbl 0306.42007
[16] R. MELROSE et N. RITTER , Interaction of nonlinear Progressing Waves (Ann. Math., 121, 1985 , p. 187-213). MR 86m:35005 | Zbl 0575.35063 · Zbl 0575.35063 · doi:10.2307/1971196
[17] W. PAWLUCKI , Le théorème de Puiseux pour une application sous-analytique (Bulletin of the Polish Academy of Sciences Mathematics, vol. 32, n^\circ 9-10, 1984 , p. 555-560). MR 86j:32015 | Zbl 0574.32010 · Zbl 0574.32010
[18] C. SABBAH , Polynômes de Bernstein-Sato à plusieurs variables (Séminaire E.D.P., exp. n^\circ 19, Ecole Polytechnique, 1986 - 1987 ). Numdam | Zbl 0634.32003 · Zbl 0634.32003
[19] J. SJÖSTRAND , Singularités analytiques microlocales (Astérisque, 95, 1982 ). MR 84m:58151 | Zbl 0524.35007 · Zbl 0524.35007
[20] M. TAMM , Subanalytic sets in the Calculus of Variations (Acta Math., vol. 146, 1981 , p. 167-199). MR 82h:32012 | Zbl 0478.58010 · Zbl 0478.58010 · doi:10.1007/BF02392462
[21] R. THOM , Ensembles et morphismes stratifiés (Bull. Am. Math. Soc., vol. 75, 1969 , p. 240-284). Article | MR 39 #970 | Zbl 0197.20502 · Zbl 0197.20502 · doi:10.1090/S0002-9904-1969-12138-5
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.