Local solvability in c∞ for quasi-linear weakly hyperbolic equations of second order

Communications in Partial Differential Equations

Volumn 21, Issue 9-10, 1996, Pages 1487-1519

  Manfrin, Renato ^a  

^a CA' FOSCARI UNIVERSITY OF VENICE   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0040062146     PISSN: 03605302     EISSN: None     Source Type: Journal    
DOI: 10.1080/03605309608821236     Document Type: Article

References (19)

1. A. Arosio and S. Spagnolo, Global existence for abstract evolution equations of weakly hyperbolic type, J. Math. pures et appl. 65 (1986), 263-305.
2. F. Colombini, E. Jannelli and S. Spagnolo, Non uniqueness in hyperbolic Cauchy problem, Ann. of Math. 126 (1987), 495-524.
3. ∞, Acta Math. 148 (1982), 243-253.
4. ∞ for a weakly hyperbolic second order equation, Rend. Sem. Mat. Univ. Padova, Vol. 91 (1994), 65-83.
5. P. D'Ancona, Gevrey well posedness of an abstract Cauchy problem of weakly hyperbolic type, Publ. RIMS Kyoto Univ. 24 (1988), 433-449.
6. P. D'Ancona and R. Manfrin, Sufficient conditions for the local solvability of some quasilinear equations of weakly hyperbolic type, Boll. U.M.I. (7) 8-D (1994), 731-754.
7. R.S. Hamilton, The inverse function theorem of Nash and Moser, Bull. A.M.S. 7 (1982), 65-222.
8. T.J.R. Hughes, T. Kato and J.E. Marsden, Well-posed quasilinear second order hyperbolic systems with applications to nonlinear elastodynamics and general relativity, Arch. Rational Mech. Anal. 63 (1977), 273-294.
9. K. Kajitani, Local solution of Cauchy problem for nonlinear hyperbolic systems in Gevrey classes, Hokkaido Math. J. 12 (1983), 434-460.
10. T. Kato, Quasilinear equations of evolution, with applications to partial differential equations, Lecture Notes in Math. 448, Springer, Berlin, 1975, 25-70.
11. N. Iwasaki, The Cauchy problem for hyperbolic equations with double characteristic, Pbl. RIMS Kyoto Univ. 19 (1983), 927-942.
12. P. Lax, Hyperbolic systems of conservation laws, II, Comm. Pure Appl. Math. 10 (1957), 537-566.
13. J. Leray and Y. Ohya, Equations et systèmes non linéaires, hyprboliques non stricts, Math. Ann. Vol.170 (1967), pp. 167-205.
14. R. Manfrin, A solvability result for a nonlinear weakly hyperbolic equation of second order, NoDEA 2 (1995), 245-264.
15. ∞ for quasi-linear weakly hyperbolic equations of second order, Preprint Dip. Mat. Pura & Appl. Univ. Padova. n. 15 (1995).
16. T. Nishitani, The Cauchy problem for weakly hyperbolic equations of second order, Comm. PDEs 5 (1980), 1273-1296.
17. T. Nishitani, A necessary and sufficient condition for the hyperbolicity of second order equations with two independent variables, J. Math. Kyoto Univ. 24 (1984), 91-104.
18. T. Nishitani, Sur les équations hyperboliques à coefficients qui sont hölderiens en t et de classe de Gevrey en x, Bull. Sc. Math. 2e série, 107 (1983), 113-138.
19. O.A. Oleinik, On the Cauchy problem for weakly hyperbolic equations, Comm. Pure Appl. Math. 23 (1970), 569-586.