MATHEMATICA BOHEMICA, Vol. 127, No. 2, pp. 301-310 (2002)

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

P. Polacik

P. Polacik, Institute of Applied Mathematics, Comenius University, Mlynska dolina, 842 48 Bratislava, Slovakia; e-mail:

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

Full text of the article:

[Previous Article] [Next Article] [Contents of this Number]
© 2005 ELibM and FIZ Karlsruhe / Zentralblatt MATH for the EMIS Electronic Edition