P. Polacik, Institute of Applied Mathematics, Comenius University, Mlynska dolina, 842 48 Bratislava, Slovakia; e-mail: polacik@fmph.uniba.sk
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 ${\R}^N$, $N\ge2$. 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 (MSC 2000): 35B40, 35K55, 35L70, 35J25
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