Some results of blow-up and formation of singularities for non-strictly hyperbolic equations

1 Alinhac, S. Blowup for Nonlinear Hyperbolic Equations Birkhäuser, Boston 1995 MR1339762

2 Colombini, F.; Del Santo, D. Development of singularities for nonlinear hyperbolic systems with periodic data Ann. Univ. Ferrara, Sez. VII-Sc. Mat., Suppl. 41 1995 15-28 MR1471012

3 Colombini, F.; Del Santo, D. Formation of singularities for nonlinear hyperbolic $2\times2$ systems with periodic data Osaka J. Math. 34 1997 99-113 MR1618673

4 Hamilton, R. S. The inverse function theorem of Nash and Moser Bull. Amer. Math. Soc. 7 1982 65-222 MR0656198

5 John, F. Formation of singularities in one dimensional nonlinear wave propagation Comm. Pure Appl. Math. 27 1974 377-405 MR0369934

6 John, F. Nonlinear Wave Equations, Formations of Singularities University Lecture Series, Amer. Math. Soc., Providence 1990 MR1066694

7 Keyfitz, B. L.; Kranzer, H. C. Non-strictly hyperbolic systems of conservation laws: formation of singularities Contemporary Math. 17 1983 77-90 MR0706089

8 Klainerman, S.; Majda, A. Formation of singularities for wave equations including the nonlinear vibrating string Comm. Pure Appl. Math. 33 1980 241-263 MR0562736

9 Keller, J. B.; Ting, L. Periodic vibrations of systems governed by nonlinear partial differential equations Comm. Pure Appl. Math. 19 1966 371-420 MR0205520

10 Lax, P. D. Hyperbolic systems of conservation laws II Comm. Pure Appl. Math. 10 1957 537-566 MR0093653

11 Lax, P. D. Development of singularities of solutions of nonlinear hyperbolic partial differential equations Jour. Math. Physics 5 1964 611-613 MR0165243

12 Liu, T.-P. Development of singularities in the nonlinear waves for quasi-linear hyperbolic partial differential equations J. Differential Equations 33 1979 92-111 MR0540819

13 Majda, A. Compressible Fluid Flow and systems of Conservation Laws in Several Space Variables Springer-Verlag, New-York 1984 MR0748308

14 Manfrin, R. Local solvability in $C^\infty$ for quasi-linear weakly hyperbolic equations of second order Comm. in PDE 21 1996 1487-1519 MR1410839

15 Manfrin, R., A note on the formation of singularities for quasi-linear hyperbolic systems, to appear in SIAM J. Math. Analysis MR1781217

16 Manfrin, R. Well posedness in the $C^\infty$ class for $u_{tt}=a(u)\Delta u$ Nonlinear Analysis 36 1999 177-212 MR1668860

17 Popivanov, P.; Slavova, A., Blow up of the solutions for quasilinear hyperbolic homogeneous systems in the plane, Preprint MR1779532

18 Saxton, R. Finite time boundary blow-up for a degenerate, quasi-linear Cauchy problem Longman Scientific & Technical Pitman Res. Notes Math. Ser. 273 1992 212-215

19 Saxton, R.; Vinod, V. Nonstrictly hyperbolic systems of partial differential equations Longman Scientific & Technical Pitman Res. Notes Math. Ser. 324 1995 239-243 MR1417079

20 Ta-tsien, L.; Kong, D. Blow-up of periodic solutions to quasilinear hyperbolic systems Nonlinear Analysis TMA 26 1996 1779-1789 MR1382544

21 Ta-tsien, L.; Zhou, Y.; Kong, D. Weak linear degeneracy and global classical solutions for general quasilinear hyperbolic systems Comm. PDE 19 1994 1263-1317 MR1284811