On growth rate near the blowup surface for semilinear wave equations

International Mathematics Research Notices

Volumn , Issue 19, 2005, Pages 1127-1155

  Merle, Frank ^a   Zaag, Hatem ^b  

^a UNIVERSITÉ DE CERGY PONTOISE   (France)

^b ÉCOLE NORMALE SUPÉRIEURE   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 20444479518     PISSN: 10737928     EISSN: None     Source Type: Journal    
DOI: 10.1155/imrn.2005.1127     Document Type: Article

References (18)

1. S. Alinhac, Blowup for Nonlinear Hyperbolic Equations, Progress in Nonlinear Differential Equations and Their Applications, vol. 17, Birkhäuser Boston, Massachusetts, 1995.
2. C. Antonini and F. Merle, Optimal bounds on positive blow-up solutions for a semilinear wave equation, Int. Math. Res. Not. 2001 (2001), no. 21, 1141-1167.
3. P. Bizoń, T. Chmaj, and Z. Tabor, On blowup for semilinear wave equations with a focusing nonlinearity, Nonlinearity 17 (2004), no. 6, 2187-2201.
4. L. A. Caffarelli and A. Friedman, The blow-up boundary for nonlinear wave equations, Trans. Amer. Math. Soc. 297 (1986), no. 1, 223-241.
5. Y. Giga and R. V. Kohn, Asymptotically self-similar blow-up of semilinear heat equations, Comm. Pure Appl. Math. 38 (1985), no. 3, 297-319.
6. _, Characterizing blowup using similarity variables, Indiana Univ. Math. J. 36 (1987), no. 1, 1-40.
7. _, Nondegeneracy of blowup for semilinear heat equations, Comm. Pure Appl. Math. 42 (1989), no. 6, 845-884.
8. F. John, Blow-up of solutions of nonlinear wave equations in three space dimensions, Manuscripta Math. 28 (1979), no. 1-3, 235-268.
9. S. Kichenassamy and W. Littman, Blow-up surfaces for nonlinear wave equations. I, Comm. Partial Differential Equations 18 (1993), no. 3-4, 431-452.
10. _, Blow-up surfaces for nonlinear wave equations. II, Comm. Partial Differential Equations 18 (1993), no. 11, 1869-1899.
11. H. Lindblad and C. D. Sogge, On existence and scattering with minimal regularity for semilinear wave equations, J. Funct. Anal. 130 (1995), no. 2, 357-426.
12. F. Merle and P. Raphael, The blow-up dynamic and upper bound on the blow-up rate for critical nonlinear Schrödinger equation, Ann. of Math (2) 161 (2005), no. 1, 157-222.
13. _, Sharp upper bound on the blow-up rate for the critical nonlinear Schrödinger equation, Geom. Funct. Anal. 13 (2003), no. 3, 591-642.
14. 2 critical nonlinear Schrödinger equation, Invent. Math. 156 (2004), no. 3, 565-672.
15. F. Merle and H. Zaag, A Liouville theorem for vector-valued nonlinear heat equations and applications, Math. Ann. 316 (2000), no. 1, 103-137.
16. _, Determination of the blow-up rate for the semilinear wave equation, Amer. J. Math. 125 (2003), no. 5, 1147-1164.
17. _, Determination of the blow-up rate for a critical semilinear wave equation, Math. Ann. 331 (2005), no. 2, 395-416.
18. J. Shatah and M. Struwe, Geometric Wave Equations, Courant Lecture Notes in Mathematics, vol. 2, Courant Institute of Mathematical Sciences, New York, and American Mathematical Society, Rhode Island, 1998.