next up previous
: この文書について... : Counterexample to global existence : Introduction and main result

Bibliography

1
R. Agemi and K. Yokoyama,
The null conditions and global existence of solutions to systems of wave equations with different propagation speeds,
``Advances in nonlinear partial differential equations and stochastics" (S. Kawashima and T. Yanagisawa ed.), Series on Adv. in Math. for Appl. Sci., Vol. 48, 43-86, World Scientific, Singapore, 1998.

2
D. Christodoulou, Global solutions of nonlinear hyperbolic equations for small initial data,
Comm. Pure Appl. Math. 39 (1986), 267-282.

3
A. Hoshiga and H. Kubo,
Global small amplitude solutions of nonlinear hyperbolic systems with a critical exponent under the null condition,
SIAM J. Math. Anal. 31 (2000), 486-513.

4
F. John,
Blow-up of solutions for quasi-linear wave equations in three space dimensions,
Comm. Pure Appl. Math. 34 (1981), 29-51.

5
S. Katayama,
Global existence for a class of systems of nonlinear wave equations in three space dimensions,
Preprint.

6
S. Katayama,
Global and almost global existence for systems of nonlinear wave equations with different propagation speeds,
Preprint.

7
S. Katayama, Global existence for systems of wave equations with nonresonant nonlinearities and null forms,
Preprint.

8
S. Klainerman,
The null condition and global existence to nonlinear wave equations, Lectures in Appl. Math. 23 (1986), 293-326.

9
M. Kovalyov,
Resonance-type behaviour in a system of nonlinear wave equations,
J. Differential Equations 77 (1989), 73-83.

10
H. Kubo and M. Ohta,
On systems of semilinear wave equations with unequal propagation speeds in three space dimensions,
Preprint.

11
K. Kubota and K. Yokoyama,
Global existence of classical solutions to systems of nonlinear wave equations with different speeds of propagation,
Japanese J. Math. 27 (2001), 113-202.

12
T. C. Sideris and S.-Y. Tu,
Global existence for systems of nonlinear wave equations in 3D with multiple speeds,
SIAM J. Math. Anal. 33 (2001), 477-488.

13
K. Yokoyama,
Global existence of classical solutions to systems of wave equations with critical nonlinearity in three space dimensions,
J. Math. Soc. Japan 52 (2000), 609-632.



Nobuki Takayama Heisei 16-1-21.