Some common asymptotic properties of semilinear parabolic, hyperbolic and elliptic equations

Poláčik, P.

Mathematica Bohemica, Tome 127 (2002) no. 2, pp. 301-310

Abstract (VO)

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 $\Omega \times (0,\infty )$.

Détail

DOI : 10.21136/MB.2002.134162

Classification : 35B40, 35G20, 35J25, 35J60, 35K55, 35L70, 37L05
Keywords: parabolic equations; elliptic equations; hyperbolic equations; asymptotic behavior; center manifold

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