On wave equations with supercritical nonlinearities

Archiv der Mathematik

Volumn 74, Issue 2, 2000, Pages 129-147

  Brenner, Philip ^a   Kumlin, Peter ^a  

^a CHALMERS UNIVERSITY OF TECHNOLOGY   (Sweden)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0034344367     PISSN: 0003889X     EISSN: None     Source Type: Journal    
DOI: 10.1007/PL00000418     Document Type: Article

References (18)

1. C. BENNET and R. SHARPLEY, Interpolation of operators. Boston 1988.
2. J. BERGH and J. LÖFSTRÖM, Interpolation spaces. Berlin-Heidelberg-New York 1976.
3. P. BRENNER, Space-time means and nonlinear Klein-Gordon equations. Report No. 1985-19, CTH/GU.
4. P. BRENNER, V. THOMÉE and L. WAHLBIN, Besov spaces and applications to difference methods for initial value problems. LNM 434. Berlin-Heidelberg-New York 1975.
5. P. BRENNER and W. VON WAHL, Global classical solutions of nonlinear wave equations. Math. Z. 176, 87-121 (1981).
6. J. GINIBRE and G. VELO, The global Cauchy problem for the non-linear Klein-Gordon equation. Math. Z. 189, 487-505 (1985).
7. M. GRILLAKIS, Regularity and asymptotic behavior of the wave equation with a critical nonlinearity. Ann. of Math. 132, 485-509 (1990).
8. M. GRILLAKIS, Regularity for the wave equation with a critical nonlinearity. Comm. Pure Appl. Math. 45, 749-774 (1992).
9. E. HEINZ und W. VON WAHL, Zu einem Satz von F. E. Browder über nichtlineare Wellengleichungen. Math. Z. 141, 33-45 (1975).
10. F. JOHN, Blow-up for quasilinear wave equation in three space dimensions. Comm. Pure Appl. Math. 33, 43-101 (1980).
11. P. KUMLIN, On mapping properties for some nonlinear operators related to hyperbolic problems. Göteborg 1985 (thesis).
12. P. KUMLIN, A Note on Maximal Rate of Decay for Solutions to Some Semilinear Wave Equations. Math. Z. 197, 465-481 (1988).
13. S. KLAINERMAN and G. PONCE, Global small amplitude solutions to nonlinear evolution equations. Commun. Pure Appl. Math. 36, 144-141 (1983).
14. J. PEETRE, Interpolation of Lipschitz operators and metric spaces. Mathematica (Cluj) 12:35, 325-334 (1970).
15. J. SHATAH and M. STRUWE, Regularity results for nonlinear wave equations. Ann. of Math. 138, 503-518 (1993).
16. 5-Klein-Gordon equations. Ann. Scuola Norm. Sup. Pisa (4) 15, 495-513 (1988).
17. M. STRUWE, Semilinear wave equations. Bull. Amer. Math. Soc. 261, 53-85 (1992).
18. W. VON WAHL, Über die klassische Lösbarkeit des Cauchy-Problems für nichtlineare Wellengleichungen bei kleinen Anfangswerten und das asymptotische Verhalten der Lösungen. Math. Z. 114, 281-299 (1970).