Asymptotic pointwise behavior for systems of semilinear wave equations in three space dimensions

Journal of Hyperbolic Differential Equations

Volumn 9, Issue 2, 2012, Pages 263-323

  Katayama, Soichiro ^a  

^a WAKAYAMA UNIVERSITY   (Japan)

Author keywords

asymptotic behavior; wave equation; Weak null condition

Indexed keywords

EID: 84861842594     PISSN: 02198916     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0219891612500099     Document Type: Article

References (24)

1. S. Alinhac, An example of blowup at infinity for a quasilinear wave equation, Astérisque 284 (2003) 1-91.
2. S. Alinhac, Remarks on energy inequalities for wave and Maxwell equations on a curved background, Math. Ann. 329 (2004) 707-722.
3. S. Alinhac, Semilinear hyperbolic systems with blowup at infinity, Indiana Univ. Math. J. 55 (2006) 1209-1232.
4. S. Asakura, Existence of a global solution to a semi-linear wave equation with slowly decreasing initial data in three space dimensions, Commun. Partial Differential Equations 11 (1986) 1459-1487.
5. D. Christodoulou, Global solutions of nonlinear hyperbolic equations for small initial data, Commun. Pure Appl. Math. 39 (1986) 267-282.
6. L. Hörmander, The lifespan of classical solutions of non-linear hyperbolic equations, in Pseudo-Differential O perators, Lecture Notes in Mathematics, Vol. 1256 (Springer-Verlag, Berlin, 1987), pp. 214-280.
7. L. Hörmander, Lectures on Nonlinear Hyperbolic Differential Equations (Springer-Verlag, Berlin, 1997).
8. F. John, Blow-up of solutions of nonlinear wave equations in three space dimensions, Manuscripta Math. 28 (1979) 235-268.
9. F. John, Blow-up of solutions for quasi-linear wave equations in three space dimensions, Commun. Pure Appl. Math. 34 (1981) 29-51.
10. F. John, Lower bounds for the life span of solutions of nonlinear wave equations in three space dimensions, Commun. Pure Appl. Math. 36 (1983) 1-35.
11. F. John, Existence for large times of strict solutions of nonlinear wave equations in three space dimensions for small initial data, Commun. Pure Appl. Math. 40 (1987) 79-109.
12. S. Katayama and H. Kubo, Asymptotic behavior of solutions to semilinear systems of wave equations, Indiana Univ. Math. J. 57 (2008) 377-400.
13. S. Katayama and H. Kubo, The rate of convergence to the asymptotics for the wave equation in an exterior domain, Funkcial. Ekvac. 53 (2010) 331-358.
14. S. Katayama and K. Yokoyama, Global small amplitude solutions to systems of nonlinear wave equations with multiple speeds, Osaka J. Math. 43 (2006) 283-326.
15. S. Klainerman, Uniform decay estimates and the Lorentz invariance of the classical wave equation, Commun. Pure Appl. Math. 38 (1985) 321-332.
16. S. Klainerman, The null condition and global existence to nonlinear wave equations, in Nonlinear Systems of Partial Differential Equations in Applied Mathematics, Part 1, Lectures in Applied Mathematics, Vol. 23 (American Mathematical Society, Providence, RI, 1986), pp. 293-326.
17. n+1, Commun. Pure Appl. Math. 40 (1987) 111-117.
18. K. Kubota and K. Yokoyama, Global existence of classical solutions to systems of nonlinear wave equations with different speeds of propagation, Japan. J. Math. (N. S.) 27 (2001) 113-202.
19. P. D. Lax and R. S. Phillips, Scattering Theory, Rev. edn. (Academic Press, New York, 1989).
20. H. Lindblad, On the lifespan of solutions of nonlinear wave equations with small initial data, Commun. Pure Appl. Math. 43 (1990) 445-472.
21. H. Lindblad and I. Rodnianski, The weak null condition for Einstein's equations, C. R. Math. Acad. Sci. Paris 336 (2003) 901-906.
22. H. Lindblad and I. Rodnianski, Global existence for the Einstein vacuum equations in wave coordinates, Commun. Math. Phys. 256 (2005) 43-110.
23. H. Sunagawa, A note on the large time asymptotics for a system of Klein-Gordon equations, Hokkaido Math. J. 33 (2004) 457-472.
24. H. Sunagawa, Large time asymptotics of solutions to nonlinear Klein-Gordon systems, Osaka J. Math. 42 (2005) 65-83.