Necessary conditions for strong hyperbolicity of first order systems
Journées équations aux dérivées partielles (1989), article no. 8, 16 p. 
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     author = {Matsumoto, Waichiro and Yamahara, Hideo},
     title = {Necessary conditions for strong hyperbolicity of first order systems},
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     eid = {8},
     pages = {1--16},
     publisher = {Ecole polytechnique},
     year = {1989},
     zbl = {0703.35100},
     mrnumber = {1030823},
     language = {en},
     url = {http://archive.numdam.org/item/JEDP_1989____A8_0/}
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Matsumoto, Waichiro; Yamahara, Hideo. Necessary conditions for strong hyperbolicity of first order systems. Journées équations aux dérivées partielles (1989), article  no. 8, 16 p. http://archive.numdam.org/item/JEDP_1989____A8_0/

1. L. Hörmander The Cauchy problem for differential equations with double characteristics, J. Analyse Math., 32, (1977) 118-196. | MR | Zbl

2. V. Ja. Ivrii Sufficient conditions for regular and completely regular hyperbolicity, Trans. Moscow Math. Soc., 1 (1978) 1-65. | Zbl

3. V. Ya. Ivrii and V.M. Petkov Necessary conditions for the Cauchy problem for non-strictly hyperbolic equations to be well-posed, Russ. Math. Surveys, 29 (1974) 1-70. | Zbl

4. N. Iwasaki The Cauchy problem for effectively hyperbolic equations, (a special case), J. Math. Kyoto Univ., 23 (1983) 503-562. | MR | Zbl

5. N. Iwasaki The Cauchy problem for effectively hyperbolic equations, (a standard type), Publ. R.I.M.S. Kyoto Univ., 20 (1984) 543-584. | MR | Zbl

6. N. Iwasaki The Cauchy problem for effectively hyperbolic equations, (general cases), J. Math. Kyoto Univ., 25 (1985) 727-743. | MR | Zbl

7. K. Kasahara and M. Yamaguti Strong hyperbolic systems of linear partial differnetial equations with constant coefficients, Mem. Coll. Sci. Univ. Kyoto, Ser. A Math., 33 (1960-1961) 1-23. | MR | Zbl

8. N.D. Koutev and V. M. Petkov Sur les systèmes régulièrement hyperboliques du premier ordre, Ann. Sofia Univ. Math. Fac., 67 (1976) 375-389. | Zbl

9. W. Matsumoto Levi condition for first order systems with characteristics of constant multiplicity, II, (in preparation).

10. T. Nishitani Système effectivement hyperbolique, Calcul opér. fronts d'ondes, Travaux en Cours 29, Hermann, Paris (1988) 108-132, ed. J. Vaillant. | MR | Zbl

11. T. Nishitani On strong hyperbolicity of systems, Hyperbolic Equations, Res. Notes Math. 158 Longman (1987) 102-114, ed. F. Colombini and M.K.V. Murthy. | MR | Zbl

12. T. Nishitani Strong hyperbolic systems with transverse propagation cone, (to appear in Note of J. Vaillant Seminar).

13. O.A. Oleinik On the Cauchy problem for weakly hyperbolic equations, Comm. Pure Appl. Math., 23 (1970) 569-586. | MR | Zbl

14. H. Yamahara On the strong hyperbolic systems, J. Math. Kyoto Univ., 27 (1987) 259-273. | MR | Zbl

15. H. Yamahara On the strong hyperbolic systems, II, (to appear in J. Math. Kyoto Univ.).

16. M.D. Bronshtein Smoothness of roots of polynomials depending on parameters, Siberian J. Math., 20 (1979). | MR | Zbl

17. T. Mandai Smoothness of roots of hyperbolic polynomials with respect to one-dimensional parameter, Bull. Fac. Gen. Ed. Gifu Univ., 21 (1985) 115-118. | MR

18. V.M. Petkov Microlocal forms for hyperbolic systems, Math. Nachr., 93 (1979) 117-131. | MR | Zbl

19. W. Matsumoto Conditions for strong hyperbolicity of first order systems.