| Abstract: |
| This talk is concerned with the large-time asymptotics for
general time-global solutions of semilinear parabolic problems defined
in ${\Bbb R}^N$. The orbit of a solution could be noncompact
in the natural
energy space $H^1({\Bbb R})$ due to the unboundedness of
${\Bbb R}$. It is proved
in this talk that every time-global solution decomposes into a
superposition of ``pseudo-traveling waves`` whose profiles are
stationary solutions.
The analysis is done within the energy space together with the
profile decomposition argument. Some applications to the analysis of
the asymptotic behavior of time-global
solutions which are treated e.g. in Chill-Jendoubi (2003),
Cortazar-del Pino-Elgueta (1999) and Feireisl-Petzeltova (1997)
are also given. |
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