Solutions explosives exceptionnelles

Alinhac, Serge

Séminaire Équations aux dérivées partielles (Polytechnique) dit aussi "Séminaire Goulaouic-Schwartz" (2005-2006), Exposé no. 19, 10 p.

[1] Alinhac S., “Blowup for Nonlinear Hyperbolic Equations”, Progr. Nonlinear Differential Equations Appl. 17, Birkhäuser Boston, Boston MA, (1995). | MR | Zbl

[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. | EuDML | Numdam | MR

[3] Alinhac S., “Explosion géométrique pour des systèmes quasi-linéaires”, Amer. J. Math. 117, (1995), 987-1017. | MR | Zbl

[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. | MR | Zbl

[5] Alinhac S., “Stability of geometric blowup”, Arch. Rat. Mech. Analysis 150, (1999), 97-125. | MR | Zbl

[6] Alinhac S., “Remarks on the blowup rate of classical solutions to quasilinear multidimensional hyperbolic systems ”, J. Math. Pure Appl. 79, (2000), 839-854. | MR | Zbl

[7] Alinhac S., “Rank two singular solutions for quasilinear wave equations”, Inter. Math. Res. Notices 18, (2000), 955-984. | MR | Zbl

[8] Alinhac S., “Exceptional Blowup Solutions to Quasilinear Wave Equations I and II”, Int. Math. Res. Notices, (2006) et preprint Orsay, (2006). | MR

[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. | Numdam | Zbl

[11] Hörmander L., “Lectures on Nonlinear Hyperbolic Differential Equations”, Math. Appl. 26, Springer Verlag, Berlin, (1997). | Zbl

[12] John F., “ Nonlinear Wave Equations, Formation of singuarities”, Univ. Lecture Ser. 2, Amer. Math. Soc. , Providence, RI, (1990). | Zbl

[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). | Zbl

[14] Lax P. D., “Hyperbolic systems of conservation laws II”, Comm. Pure Appl. Math. 10, (1957), 537-566. | Zbl

[15] Majda A., “Compressible fluid flow and systems of conservation laws ”, Appl. Math. Sc. 53, Springer Verlag, New-York (1984). | Zbl

[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. | Zbl

[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. | Zbl

[18] Merle F. et Zaag H., “Determination of the blowup rate for the semilinear wave equation”, Amer. J. Math. 125, (2003), 1147-1164. | Zbl

[19] Merle F. et Zaag H., “Determination of the blowup rate for a critical semilinear wave equation”, Math. Ann. 331, (2005), 395-416. | Zbl

[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. | Zbl

[21] Perelman G., “On the blowup phenomenon for the critical nonlinear Schrödinger equation in 1D”, Ann. Inst. H. Poincaré 2, (2001), 605-673. | Zbl

[22] Raphaël P., “Stability of the log-log bound for blowup solutions to the critical nonlinear Schrödinger equation”, Math. Annalen 331, (2005), 577-609. | Zbl