On a weakly hyperbolic quasilinear mixed problem of second order

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1. [1] R.A. Adams, "Sobolev spaces", Academic Press[A subsidiary of Harcourt Brace Jovanovich, Publishers], New York- London, 1975, Pure and Applied Mathematics, Vol. 65. Zbl0314.46030MR450957
2. [2] R.G. A, A mixed problem for second order hyperbolic equations, Izv. Akad. Nauk Armjan. SSR Ser. Mat.12 (1977), 32-45, 85. Zbl0359.35046MR460906
3. [3] P. D'Ancona - M. Di Flaviano, An abstract degenerate hyperbolic equation with application to mixed problems, Hokkaido Math. J. (2) 29 (2000), 315-328. Zbl0974.35081MR1776711
4. [4] P. D'Ancona - R. Manfrin, A class of locally solvable semilinear equations of weakly hyperbolic type, Ann. Mat. Pura Appl. 168 (1995), 355-372. Zbl0849.35076MR1378250
5. [5] P. D'Ancona - R. Racke, Weakly hyperbolic equations in domains with boundaries, Nonlinear Anal.33 (1998), 455-472. Zbl0933.34067MR1635708
6. [6] R.S. Hamilton, The inverse function theorem of Nash and Moser, Bull. Amer. Math. Soc. (1) 7 (1982), 65-222. Zbl0499.58003MR656198
7. [7] L. Hörmander, "The analysis of linear partial differential operators", second ed., Springer-Verlag, Berlin, 1990. Zbl0687.35002
8. [8] K. Kimura, A mixed problem for weakly hyperbolic equations of second order, Comm. Partial Differential Equations6 (1981), 1335-1361. Zbl0492.35052MR640160
9. [9] M.L. Krasnov, Mixed boundary problems for degenerate linear hyperbolic differential equations second order, Mat. Sb.49 (1959), 29-84. Zbl0143.33202MR118954
10. [10] A. Kubo, Mixed problems for some weakly hyperbolic second order equations, Math. Japonica (5) 29 (1984), 721-751. Zbl0599.35110MR768857
11. [11] A. Kubo, On the mixed problems for weakly hyperbolic equations of second order, Comm. Partial Differential Equations (9) 9 (1984), 889-917. Zbl0548.35076MR749651
12. [12] A. Kubo, Well posedness for the mixed problems of degenerate hyperbolic equations, Funkcialaj Ekvacioj34 (1991), 95-102. Zbl0789.35115MR1116882
13. [13] J.-L. Lions - E. Magenes, "Non-homogeneous boundary value problems and applications", Vol. II. Die Grundlehren der mathematischen Wissenschaften. Springer-Verlag, New York-Heidelberg, 1972. Zbl0223.35039MR350178
14. [14] V.A. Malovichko, Boundary value problems for degenerate and nondegenerate hyperbolic systems, Differentsial' nye Uravneniya25 (1989) 1977-1981, 2022. MR1034105
15. [15] O.A. Oleinik, The Cauchy problem and the boundary value problem for second order hyperbolic equations degenerating in a domain and on its boundary, Soviet Math. Dokl. (3) 7 (1966), 969-977. Zbl0173.37601
16. [16] O.A. Oleinik, On the Cauchy problem for weakly hyperbolic equations, Comm.Pure Appl. Math.23 (1970), 569-586. MR264227
17. [17] R. Sakamoto, "Hyperbolic boundary value problems", Cambridge University Press, Cambridge, 1982. Zbl0494.35002MR666700