Sufficient conditions are given so that the solutions of the initial‐boundary value problem for the nonlinear Klein–Gordon equation do not exist for all t≳0.
Topics
Klein-Gordon equation
REFERENCES
1.
R.
Glassey
, “Blow-up theorems for nonlinear wave equations
,” Math. Z.
132
, 182
–203
(1973
).2.
F.
John
, “Blowup of solutions of nonlinear wave equations in three space dimensions
,” Manuscr. Math.
28
, 235
–268
(1979
).3.
M.
Tsutsumi
, “Nonexistence of global solutions to the Cauchy problem for the damped nonlinear Schrödinger equations
,” SIAM J. Math. Anal.
15
, 357
–366
(1984
).4.
J.
Bona
and J.-C.
Saut
, “Dispersive blowup of solutions of generalized Korteweg-de Vries equations
,” J. Diff. Equations
103
, 3
–57
(1993
).5.
M. Reed, Abstract Nonlinear Wave Equations, Lecture notes in Mathematics Vol. 507 (Springer-Verlag, Berlin, 1976).
6.
O. Ladyzhenskaya, V. Solonnikov, and N. Ural’tseva, Linear and Qu asilinear Equations of Parabolic Type (Nauka, Moscow, 1967) (in Russian).
7.
A. Friedman, Partial Differential Equations (Holt, Rinehart, and Winston, New York, 1969).
8.
P.
Kelley
, “Self-focusing of optical beams
,” Phys. Rev. Lett.
15
, 1005
–1008
( 1965
).9.
V.
Zakharov
, V.
Sobolev
, and V.
Synakh
, “Behavior of light beams in nonlinear media
,” Sov. Phys. JETP
33
, 77
–81
(1971
).
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© 1995 American Institute of Physics.
1995
American Institute of Physics
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