×

Micro-hyperbolic systems. (English) Zbl 0413.35049


MSC:

35L55 Higher-order hyperbolic systems
35S10 Initial value problems for PDEs with pseudodifferential operators
35D05 Existence of generalized solutions of PDE (MSC2000)
35D10 Regularity of generalized solutions of PDE (MSC2000)
35N99 Overdetermined problems for partial differential equations and systems of partial differential equations
46F15 Hyperfunctions, analytic functionals
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Anderson, K. G., Analytic wave front sets for solutions of linear partial differential equations of principal type.Trans. Amer. Mat. Soc., 176 (1973), 5–22.
[2] Bony, J. M., Extension du théorème de Holmgren. Sem. Goulaouic-Schwartz 1975–76, exposé 17.
[3] Bony J. M., &Schapira, P., Existence et prolongement des solutions holomorphes des équations aux dérivées partielles.Inventiones Math., 17 (1972), 95–105. · Zbl 0225.35008 · doi:10.1007/BF01418934
[4] Bony, J. M. &Schapir, P.,Solutions hyperfonctions du problème de Cauchy. Lecture Notes in Math. Springer, 287 (1973), 82–98. · doi:10.1007/BFb0068146
[5] –, Propagation des singularités analytiques pour les solutions des équations aux dérivées partielles.Ann. Inst. Fourier, 26 (1976), 81–140. · Zbl 0312.35064
[6] Gårding, L., Linear hyperbolic partial differential equations with constant coefficients.Acta Math. 85 (1950), 1–62. · Zbl 0045.20202 · doi:10.1007/BF02395740
[7] Hadamard, J.,Lectures on Cauchy’s Problem in Linear Partial Differential Equations, Yale Univ. Press, 1923. Reprinted by Dover, New York. · JFM 49.0725.04
[8] Hamada, Y., The singularities of the solutions of the Cauchy problem.Publ. R.I.M.S., Kyoto University, 5, 20–40 (1969). · Zbl 0203.40702
[9] Hamada, Y., Leray, J. &Wagschal, C., Systèmes d’équations aux dérivées partielles à caractéristiques multiples: Problème de Cauchy ramifié, hyperbolicité partielle.J. Math. Pures et Appl., 55 (1976), 297–352. · Zbl 0307.35056
[10] Hironaka, H., Subanalytic sets, Number theory, Algebraic geometry, and Commutative algebra in honor of Y. Akizuki, 453–495, Kinokunyia Publications, Tokyo, 1975.
[11] Hörmander L., Uniqueness theorem and wave front sets for solutions of linear differential equations with analytic coefficients.Comm. Pure Appl. Math., 24 (1971), 617–704. · Zbl 0221.47029 · doi:10.1002/cpa.3160240503
[12] Hörmander, L., The Cauchy problem for differential equations with double characteristics.J. Analyse Math., 32 (1977), 118–196. · Zbl 0367.35054 · doi:10.1007/BF02803578
[13] Ivrii, V. &Pietkov, V., Necessary conditions for the Cauchy problem for non-strictly hyperbolic equations to be well-posed.Uspeki Mat Nauk, 29 (1974), 5. · Zbl 0312.35049
[14] Kashiwara, M., Algebraic study of systems of partial differential equations (thesis), Univ. of Tokyo, 1971 (in Japanese).
[15] –, On the maximally overdetermined systems of linear differential equations I.Publ. R.I.M.S., Kyoto University, 10 (1975), 563–579. · Zbl 0313.58019 · doi:10.2977/prims/1195192011
[16] Kashiwara, M. &Kawai, T., On the boundary value problem for elliptic system of linear differential equations, II.Proc. Japan Acad. 49 (1973), 164–168. · Zbl 0279.35037 · doi:10.3792/pja/1195519397
[17] – Microhyperbolic pseudodifferential operators I.J. Math. Soc. Japan, 27 (1975), 359–404. · Zbl 0305.35066 · doi:10.2969/jmsj/02730359
[18] –, Finiteness theorem for holonomic systems of microdifferential equations.Proc. Japan Acad., 52 (1976), 341–343. · Zbl 0361.35064 · doi:10.3792/pja/1195518268
[19] Kashiwara, M. &Schapira, P., Probleme de Cauchy pour les systemes microdifferentials dans le domaine complexe.Inventiones Math., 46 (1978), 17–38. · Zbl 0369.35061 · doi:10.1007/BF01390101
[20] Leray, J.,Hyperbolic Differential Equations. The Institute for Advance Study, Princeton, 1952.
[21] Mizohata, S., Analyticity of solutions of hyperbolic systems with analytic coefficients.Comm. Pure Appl. Math., 14 (1961), 547–559. · Zbl 0105.07203 · doi:10.1002/cpa.3160140326
[22] Petrowsky, I. G., Über das Cauchysche Problem für Systeme von partiellen Differentialgleichungen.Mat. Sbornik, 44 (1937), 815–868. · Zbl 0018.40503
[23] Sato, M. &Kashiwara, M., The determinant of matrices of pseudo-differential operators.Proc. Japan Acad., 51 (1975), 17–19. · Zbl 0337.35067 · doi:10.3792/pja/1195518723
[24] Sato, M., Kashiwara, M. &Kawai, T.,Hyperfunctions and pseudo-differential equations. Lecture Notes in Math 287, Springer, 265–529 (1973). · Zbl 0277.46039
[25] Whitney, H., Tangents to an analytic variety.Ann. of Math., 81 (1964), 496–549. · Zbl 0152.27701 · doi:10.2307/1970400
[26] Grothendieck, A., Elements de Geometrie Algebrique III.Publ. Math. I.H.E.S., 11 (1961). · Zbl 0235.14007
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.