Some results of Gevrey and analytic regularity for semilinear weakly hyperbolic equations of Oleinik type

 Access to full text

 Full (PDF)

1. [A] R.A. Adams, Sobolev Spaces, Academic Press (1975). Zbl0314.46030MR450957
2. [AM] S. Alinhac - G. Métivier, Propagation de l'analyticité des solutions de système hyperboliques nonlinéaires, Inv. Math., 75 (1984), pp. 189-203. Zbl0545.35063MR732545
3. [AS] A. Arosio - S. Spagnolo, Global existence for abstract evolution equations of weakly hyperbolic type, J. Math. Pures Appl., 65 (1986), pp. 263-305. Zbl0616.35049MR875159
4. [C] L. Cardosi, Evolution equations in scales of abstract Gevrey spaces, Boll. Un. Mat. Ital., 6 (1985), pp. 379-406. Zbl0612.35120MR805227
5. [CDS] F. Colombini - E. De Giorgi - S. Spagnolo, Sur les équations hyperboliques avec des coefficients qui ne dépendent que du temps, Ann. Scu. Norm. Sup. Pisa, 6 (1979), pp. 511-559. Zbl0417.35049MR553796
6. [CJS1] F. Colombini - E. Jannelli - S. Spagnolo, Non uniqueness in hyperbolic Cauchy problem, Ann. Math., 126 (1987), pp. 495-524. Zbl0649.35051MR916717
7. [CJS2] F. Colombini - E. Jannelli - S. Spagnolo, Well posedness in the Gevrey classes of the Cauchy problem for a non strictly hyperbolic equation with coefficients depending on time, Ann. Scu. Norm. Sup. Pisa, 10 (1983), pp. 291-312. Zbl0543.35056MR728438
8. [CS] F. Colombini - S. Spagnolo, An example of a weakly hyperbolic Cauchy problem not well posed in C∞, Acta Math., 148 (1982), pp. 243-253. Zbl0517.35053
9. [D] P. D'Ancona, Gevrey well posedness of an abstract Cauchy problem of weakly hyperbolic type, Publ. RIMS Kyoto Univ., 24 (1988), pp. 433-449. Zbl0706.35077MR966182
10. [DM] P. D'Ancona - R. Manfrin, Local solvability for a class of semilinear weakly hyperbolic equations, to appear Ann. Mat. Pura Appl. Zbl0849.35076
11. [H] L. Hörmander, Uniqueness theorems and wave front sets for solutions of linear differential equations with analytic coefficients, Comm. Pure Appl. Math., 24 (1971), pp. 671-704. Zbl0226.35019MR294849
12. [K] T. Kato, The Cauchy problem for quasilinear symmetric hyperbolic systems, Arch. Rat. Mech. Anal., 58 (1975), pp. 181-205. Zbl0343.35056MR390516
13. [J1] E. Jannelli, Analytic solutions of non linear hyperbolic systems, Boll. Un. Mat. Ital. (6), 5-B (1986), pp. 487-501. Zbl0612.35083MR860640
14. [J2] E. Jannelli, Gevrey well posedness for a class of weakly hyperbolic equations, J. Math. Kyoto Univ., 24 (1984), pp. 763-778. Zbl0582.35070MR775986
15. [LO] J. Leray - Y. Ohya, Systèmes nonlinéaires hyperboliques nonstrictes, Math. Ann., 70 (1967), pp. 167-205. Zbl0146.33701MR208136
16. [M1] S. Mizohata, The Theory of Partial Differential Equations, University Press, Cambridge (1973). Zbl0263.35001MR599580
17. [M2] S. Mizohata, On the Cauchy Problem, Academic Press (1985). Zbl0616.35002MR860041
18. [M3] S. Mizohata, Analyticity of solutions of hyperbolic systems with analytic coefficients, Comm. Pure Appl. Math., 14 (1961), pp. 547-559. Zbl0105.07203MR132919
19. [N1] T. Nishitani, Energy inequality for nonstrictly hyperbolic operators in Gevrey classes, J. Math. Kyoto Univ., 24 (1983), pp. 739-773. Zbl0552.35051MR728159
20. [N2] T. Nishitani, Sur les équations hyperboliques à coefficients qui sont holderiens en t et de classe de Gevrey en x, Bull. Sci. Math.2e série, 107 (1983), pp. 113-138. Zbl0536.35042MR704720
21. [N3] T. Nishitani, A necessary and sufficient condition for the hyperbolicity of second order equations with two indipendent variables, J. Math. Kyoto Univ., 24 (1984), pp. 91-104. Zbl0552.35049MR737827
22. [O1] O.A. Oleinik, On the Cauchy problem for weakly hyperbolic equations, Comm. Pure Appl. Math., 23 (1970), pp. 569-586. MR264227
23. [O2] O.A. Oleinik, Linear equations of second order with non negative characteristic form, Mat. Sb., 61 (1966), pp. 111-140 (English transl.: Transl. Am. Math. Soc. (2) 65, pp. 167-199). MR193383
24. [OT] Y. Ohya - S. Tarama, Le problème de Cauchy a caractéristiques multiples dans la classe de Gevrey (coéfficients hölderiens en t), Proceedings of the Conference on Hyperbolic Equations and Related Topics, Kinokuniya, Tokyo, 1985. Zbl0665.35045
25. [S1] S. Spagnolo, Analytic regularity of the solutions of a semilinear weakly hyperbolic equation, Ric. Mat. Suppl., 36 (1987), pp. 193-202. Zbl0692.35020MR956027
26. [S2] S. Spagnolo, Some results of analytic regularity for the semi-linear weakly hyperbolic equations of the second order, Rend. Sem. Mat. Univ. Pol. Torino, Fascicolo Speciale 1988, Hyperbolic Equations (1987), pp. 203-329. Zbl0694.35018MR1007377
27. [S3] S. Spagnolo, Analytic and Gevrey Well-Posedness of the Cauchy Problem for Second Order Weakly Hyperbolic Equations with Coefficients Irregular in Time, Taniguchi Symp. HERT, Katata (1984), pp. 363-380. Zbl0679.35057MR925258