Affiliation:
1. Department of Mathematics, Hokkaido UniversitySapporo 060-0810, Japan
Abstract
We study the existence and scattering of global small amplitude solutions to modified improved Boussinesq equations in one dimension with nonlinear term
behaving as a power
as
. Solutions are considered in
space for all
. According to the value of
s
, the power nonlinearity exponent
p
is determined. Liu (Liu 1996
Indiana Univ. Math. J
.
45
, 797–816) obtained the minimum value of
p
greater than 8 at
for sufficiently small Cauchy data. In this paper, we prove that
p
can be reduced to be greater than
at
and the corresponding solution
u
has the time decay, such as
as
. We also prove non-existence of non-trivial asymptotically free solutions for
under vanishing condition near zero frequency on asymptotic states.
Subject
General Physics and Astronomy,General Engineering,General Mathematics
Cited by
14 articles.
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