We consider two problems in the asymptotic behavior of
semilinear second order wave equations. First, we consider the
scattering theory for the energy log-subcritical wave equation
in
, where
has logarithmic
growth at
.
We discuss the solution with general (respectively spherically symmetric) initial data
in the logarithmically weighted (respectively lower regularity) Sobolev space. We also
include some observation about scattering in the energy subcritical case. The
second problem studied involves the energy log-supercritical wave equation
in
.
We prove the same results of global existence and
scattering for this equation with a slightly higher power of the logarithm factor in the
nonlinearity than that allowed in previous work by Tao (J. Hyperbolic Differ. Equ.,
4:2 (2007), 259–265).
