Abstract
It is shown that solutions of the nonlinear Klein-Gordon equation
u
tt
- ∆
u
+
mu
+
P
'(
u
) = 0 decay to zero in the local
L
2
mean if the initial energy is bounded provided
s
P
')
s
) - 2
P
(
s
) ≥
a
P
(
s
) ≥ 0 with
a
> 0. The local energy also decays. The proof is based on manipulating energy identities and requires that
u
have continuouś first derivatives and piecewise continuous second derivatives. The proof is also applicable to certain systems of equations.
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