Solutions explosives exceptionnelles

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1. Alinhac S., “Blowup for Nonlinear Hyperbolic Equations”, Progr. Nonlinear Differential Equations Appl. 17, Birkhäuser Boston, Boston MA, (1995). Zbl0820.35001
2. Alinhac S., “ A minicourse on global existence and blowup of classical solutions to multidimensional quasilinear wave equations”, Journées “Equations aux Dérivées partielles” (Forges les Eaux, 2002). Université de Nantes, Nantes, 2002. http://www.math.sciences.univ-nantes.fr/edpa. 
3. Alinhac S., “Explosion géométrique pour des systèmes quasi-linéaires”, Amer. J. Math. 117, (1995), 987-1017. Zbl0840.35060
4. Alinhac S., “Blowup of small data solutions for a class of quasilinear wave equations in two space dimensions, II”, Acta Math. 182, (1999), 1-23. Zbl0973.35135
5. Alinhac S., “Stability of geometric blowup”, Arch. Rat. Mech. Analysis 150, (1999), 97-125. Zbl0962.35119
6. Alinhac S., “Remarks on the blowup rate of classical solutions to quasilinear multidimensional hyperbolic systems ”, J. Math. Pure Appl. 79, (2000), 839-854. Zbl0979.35092
7. Alinhac S., “Rank two singular solutions for quasilinear wave equations”, Inter. Math. Res. Notices 18, (2000), 955-984. Zbl0971.35053
8. Alinhac S., “Exceptional Blowup Solutions to Quasilinear Wave Equations I and II”, Int. Math. Res. Notices, (2006) et preprint Orsay, (2006). Zbl1134.35381
9. Alinhac S., “A Numerical Study of Blowup for Wave Equations with Gradient Terms”, preprint, Orsay, (2006). 
10. Bourgain J., Wang W., “Construction of blowup solutions for the nonlinear Schödinger equation with critical nonlinearity”, Ann. Scuola Norm. Sup. Pisa Cl. Sc. 25, (1997), 197-215. Zbl1043.35137
11. Hörmander L., “Lectures on Nonlinear Hyperbolic Differential Equations”, Math. Appl. 26, Springer Verlag, Berlin, (1997). Zbl0881.35001
12. John F., “ Nonlinear Wave Equations, Formation of singuarities”, Univ. Lecture Ser. 2, Amer. Math. Soc. , Providence, RI, (1990). Zbl0716.35043
13. Klainerman S., “The null condition and global existence to nonlinear wave equations”, in Nonlinear Systems of Partial Differential Equations in Applied Mathematics, Part 1 ( Santa Fe, NM, 1984), 293-326. Lect. Appl. Math. 23, Amer. Math. Soc. , Providence, RI, (1986). Zbl0599.35105
14. Lax P. D., “Hyperbolic systems of conservation laws II”, Comm. Pure Appl. Math. 10, (1957), 537-566. Zbl0081.08803
15. Majda A., “Compressible fluid flow and systems of conservation laws ”, Appl. Math. Sc. 53, Springer Verlag, New-York (1984). Zbl0537.76001
16. Merle F., “Construction of solutions with exactly k blowup points for the Schrödinger equation with critical nonlinearity”, Comm. Math. Physics 129, (1990), 223-240. Zbl0707.35021
17. Merle F. et Raphaël P., “On a sharp lower bound on the blowup rate for the $L^2$ critical nonlinear Schrödinger equation”, J. Amer. Math. Soc. 19, (2006), 37-90. Zbl1075.35077
18. Merle F. et Zaag H., “Determination of the blowup rate for the semilinear wave equation”, Amer. J. Math. 125, (2003), 1147-1164. Zbl1052.35043
19. Merle F. et Zaag H., “Determination of the blowup rate for a critical semilinear wave equation”, Math. Ann. 331, (2005), 395-416. Zbl1136.35055
20. Merle F. et Zaag H., “On growth rate near the blowup surface for semilinear wave equations”, Intern. Math. Res. Notices 19, (2005), 1127-1155. Zbl1160.35478
21. Perelman G., “On the blowup phenomenon for the critical nonlinear Schrödinger equation in 1D”, Ann. Inst. H. Poincaré 2, (2001), 605-673. Zbl1007.35087
22. Raphaël P., “Stability of the log-log bound for blowup solutions to the critical nonlinear Schrödinger equation”, Math. Annalen 331, (2005), 577-609. Zbl1082.35143