Article
MSC:
35B40,
35G20,
35J25,
35J60,
35K55,
35L70,
37L05 | MR 1981535 | Zbl 1010.35009 | DOI: 10.21136/MB.2002.134162
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Keywords:
parabolic equations; elliptic equations; hyperbolic equations; asymptotic behavior; center manifold
parabolic equations; elliptic equations; hyperbolic equations; asymptotic behavior; center manifold
Summary:
We consider three types of semilinear second order PDEs on a cylindrical domain $\Omega \times (0,\infty )$, where $\Omega $ is a bounded domain in ${{\mathbb{R}}}^N$, $N\ge 2$. Among these, two are evolution problems of parabolic and hyperbolic types, in which the unbounded direction of $\Omega \times (0,\infty )$ is reserved for time $t$, the third type is an elliptic equation with a singled out unbounded variable $t$. We discuss the asymptotic behavior, as $t\rightarrow \infty $, of solutions which are defined and bounded on $\Omega \times (0,\infty )$.
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