Solutions explosives exceptionnelles

Serge Alinhac[1]

  • [1] Département de Mathématiques, Université Paris-Sud, 91405 Orsay, France

Séminaire Équations aux dérivées partielles (2005-2006)

  • Volume: 2005-2006, page 1-10

How to cite


Alinhac, Serge. "Solutions explosives exceptionnelles." Séminaire Équations aux dérivées partielles 2005-2006 (2005-2006): 1-10. <>.

affiliation = {Département de Mathématiques, Université Paris-Sud, 91405 Orsay, France},
author = {Alinhac, Serge},
journal = {Séminaire Équations aux dérivées partielles},
keywords = {waves equations; explosive solutions; instability},
language = {fre},
pages = {1-10},
publisher = {Centre de mathématiques Laurent Schwartz, École polytechnique},
title = {Solutions explosives exceptionnelles},
url = {},
volume = {2005-2006},
year = {2005-2006},

AU - Alinhac, Serge
TI - Solutions explosives exceptionnelles
JO - Séminaire Équations aux dérivées partielles
PY - 2005-2006
PB - Centre de mathématiques Laurent Schwartz, École polytechnique
VL - 2005-2006
SP - 1
EP - 10
LA - fre
KW - waves equations; explosive solutions; instability
UR -
ER -


  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. 
  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

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