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

Poláčik, Peter

Displaying similar documents to “Some common asymptotic properties of semilinear parabolic, hyperbolic and elliptic equations”

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

Peter Poláčik (2002)

Mathematica Bohemica

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We consider three types of semilinear second order PDEs on a cylindrical domain $Ω \times (0, \infty)$ , where $Ω$ is a bounded domain in $ℝ^{N}$ , $N \geq 2$ . Among these, two are evolution problems of parabolic and hyperbolic types, in which the unbounded direction of $Ω \times (0, \infty)$ 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 $Ω \times (0, \infty)$ .

Asymptotic behavior of solutions of semilinear elliptic equations on an unbounded strip.

Brunovský, P., Mora, X., Poláčik, P., Solà-Morales, J. (1991)

Acta Mathematica Universitatis Comenianae. New Series

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Realization of the dynamics of ODE's in scalar parabolic PDE's

Poláčik, Peter

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Convergence to a positive equilibrium for some nonlinear evolution equations in a ball.

Haraux, A., Poláčik, P. (1992)

Acta Mathematica Universitatis Comenianae. New Series

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A priori bounds for solutions of parabolic problems and applications

Pavol Quittner (2002)

Mathematica Bohemica

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We review some recent results concerning a priori bounds for solutions of superlinear parabolic problems and their applications.