Abstract: We consider three types of semilinear second order PDEs on a cylindrical domain $\Omega \times (0,\infty )$, where $\Omega $ is a bounded domain in ${\R }^N$, $N\ge 2$. 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\to \infty $, of solutions which are defined and bounded on $\Omega \times (0,\infty )$.
Keywords: parabolic equations, elliptic equations, hyperbolic equations, asymptotic behavior, center manifold
Classification (MSC2000): 35B40, 35K55, 35L70, 35J25
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